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  • 1.
    Baek, Seung Ki
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Cluster Monte Carlo study of magnetic dipoles2011Inngår i: Journal of the Korean Physical Society, ISSN 0374-4884, E-ISSN 1976-8524, Vol. 59, nr 3, s. 2381-2386Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We implement a cluster-update Monte Carlo algorithm to simulate magnetic dipoles of the XY-spin type, confined in the two-dimensional plane. The long-range character and anisotropy in the dipole interaction are handled by the Luijten-Bl\"ote algorithm and the Dotsenko-Selke-Talapov algorithm, respectively. We have checked performance of this algorithm in comparison to the Metropolis algorithm and found that it equilibrates the system faster in terms of the number of flipped spins, although the overall computational complexity of the problem remains the same.

  • 2.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Bernhardsson, Sebastian
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Equilibrium solution to the lowest unique positive integer game2010Inngår i: Fluctuation and Noise Letters, ISSN 0219-4775, E-ISSN 1793-6780, Vol. 9, nr 1, s. 61-68Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a precise analysis in previous works. We here present a systematic way to reach the solution for a general number of players, and show that this game is an example of conflict between the group and the individual interests.

  • 3.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Bernhardsson, Sebastian
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Zipf's law unzipped2011Inngår i: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 13, s. 043004-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups the unique words, or the elements could be inhabitants and the groups the cities in a country, and so on. A Random Group Formation (RGF) is presented from which a Bayesian estimate is obtained based on minimal information: it provides the best prediction for the number of groups with $k$ elements, given the total number of elements, groups, and the number of elements in the largest group. For each specification of these three values, the RGF predicts a unique group distribution $N(k)\propto \exp(-bk)/k^{\gamma}$, where the power-law index $\gamma$ is a unique function of the same three values. The universality of the result is made possible by the fact that no system specific assumptions are made about the mechanism responsible for the group division. The direct relation between $\gamma$ and the total number of elements, groups, and the number of elements in the largest group, is calculated. The predictive power of the RGF model is demonstrated by direct comparison with data from a variety of systems. It is shown that $\gamma$ usually takes values in the interval $1\leq\gamma\leq 2$ and that the value for a given phenomena depends in a systematic way on the total size of the data set. The results are put in the context of earlier discussions on Zipf's and Gibrat's laws, $N(k)\propto k^{-2}$ and the connection between growth models and RGF is elucidated.

  • 4.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Choi, Jung-Kyoo
    Kim, Beom Jun
    Dworkin's Paradox2012Inngår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 7, nr 6, s. e38529-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    How to distribute welfare in a society is a key issue in the subject of distributional justice, which is deeply involved with notions of fairness. Following a thought experiment by Dworkin, this work considers a society of individuals with different preferences on the welfare distribution and an official to mediate the coordination among them. Based on a simple assumption that an individual's welfare is proportional to how her preference is fulfilled by the actual distribution, we show that an egalitarian preference is a strict Nash equilibrium and can be favorable even in certain inhomogeneous situations. These suggest how communication can encourage and secure a notion of fairness.

  • 5.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Critical condition of the water-retention model2012Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, nr 3, s. 032103-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study how much water can be retained without leaking through boundarieswhen each unit square of a two-dimensional lattice is randomly assigned a blockof unit bottom area but with different heights from zero to $n-1$.As more blocks are put into the system,there exists a phase transition beyond whichthe system retains a macroscopic volume of water.We locate the critical points and verify that the criticalitybelongs to the two-dimensional percolation universality class.If the height distribution can be approximated as continuous for large $n$,the system is always close to a critical point and the fraction of the areabelow the resulting water level is given by the percolation threshold.This provides a universal upper bound ofareas that can be covered by water in a random landscape.

  • 6.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan Univ., Suwon, Korea.
    Numerical Study of Game Theory2010Inngår i: New Physics, ISSN 0374-4914, Vol. 60, nr 9, s. 943-951Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    Game-theoretic approach has been providing a powerful tool in qualitative understanding of macroscopic social phenomena in social sciences, e.g., in economics and political science. Recently, researchers in physics, especially in statistical physics, use these game-theoretic approaches but in more quantitative way and have been producing a variety of interesting results in the new research area called ’sociophysics’ by studying human society as a complex system. This work introduces recent works that have tackled combinatorial complexities arising in game-theoretic studies with the aid of simplified assumptions and numerical computations. We first show how cooperation emerges in the prisoner’s dilemma game when each player’s memory capacity is enhanced and suggest that the intelligent tit-for-tat strategy plays a crucial role in the history of cooperation. And then it is numerically shown that there is a certain case of simultaneous coordination among many players where the system has a high risk of failure when everyone is willing to follow the coordination, which is actually higher than when some are not concerned about it. Lastly, we discuss mathematical treatment of an equilibrium solution for a reverse auction game, which is a variant of the minority game, and its computational approach.

  • 7.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Bounds of percolation thresholds in the enhanced binary tree2011Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 390, nr 8, s. 1447-1452Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is argued that the lower critical percolation threshold of the enhanced binary tree is bounded as $p_{c1} < 0.355~059$ by studying its subgraphs while the upper threshold is bounded both from above and below by $1/2$ according to renormalization-group arguments. We also review a correlation analysis in an earlier work, which claimed a significantly higher estimate of $p_{c2}$ than $1/2$, to show that this analysis in fact gives a consistent result with this bound. It confirms that the duality relation between critical thresholds does not hold exactly for the EBT and its dual, possibly due to the lack of transitivity.

  • 8.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Hierarchical renormalization-group study on the planar bond-percolation problem2011Inngår i: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 83, nr 5, s. 055601-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    For certain hierarchical structures, one can study the percolation problemusing the renormalization-group method in a very precise way.We show that the idea can be alsoapplied to two-dimensional planar lattices by regarding them as hierarchicalstructures. Either a lower bound or an exact critical probability can beobtained with this method and the correlation-length critical exponent isapproximately estimated as $\nu \approx 1$.

  • 9.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Non-Kosterlitz-Thouless transitions for the q-state clock models2010Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 82, nr 3, s. 031102-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The $q$-state clock model with the cosine potential has a single phasetransition for $q\leq4$ and two transitions for $q\geq5$. It is shown byMonteCarlo simulations that the helicity modulus for the five-state clock model($q=5$) does not vanish at the high-temperature transition. This is incontrast to the clock models with $q\geq6$ for which the helicity modulusvanishes. This means that the transition for the five-state clock modeldiffers from the Kosterlitz-Thouless (KT) transition. It is also shown thatthis change in the transition is caused by an interplay between the numberof angular directions and the interaction potential: by slightly modifyingthe interaction potential, the KT transition for $q=6$ turns into the samenon-KT transition. Likewise, the KT transition is recovered for $q=5$ whenthe Villain potential is used. Comparisons with other clock-model resultsare made and discussed.

  • 10.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Bernhardsson, Sebastian
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Choi, Kweon
    Gyeonggi Science High School.
    Kim, Beom Jun
    Department of Energy Science and BK21 Physics Research Division, Sungkyunkwan University, Suwon 440-746, Korea.
    Flow improvement caused by agents who ignore traffic rules2009Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 80, nr 1, s. 016111-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A system of agents moving along a road in both directions is studied numerically within a cellular-automata formulation. An agent steps to the right with probability $q$ or to the left with $1-q$ when encountering other agents. Our model is restricted to two agent types, traffic-rule abiders ($q=1$) and traffic-rule ignorers ($q=1/2$). The traffic flow, resulting from the interaction between these two types of agents, is obtained as a function of density and relative fraction. The risk for jamming at a fixed density, when starting from a disordered situation, is smaller when every agent abides by a traffic rule than when all agents ignore the rule. Nevertheless, the absolute minimum occurs when a smallfraction of ignorers are present within a majority of abiders. The characteristic features for the spatial structure of the flow pattern are obtained and discussed.

  • 11.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Kim, Beom Jun
    BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea.
    Comment on `Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'2009Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 42, s. 478001-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds $p_{c1}$ and $p_{c2}$ with $p_{c1}<p_{c2}$. Our Monte Carlo study implies that the second threshold $p_{c2}$ is significantly lower than a recent claim by Nogawa and Hasegawa (J. Phys. A: Math. Theor. {\bf 42} (2009) 145001). This means that $p_{c2}$ for the EBT does not obey the duality relation for the thresholds of dual graphs $p_{c2}+\overline{p}_{c1}=1$ which is a property of a transitive, nonamenable, planar graph with one end. As in regular hyperbolic lattices, this relation instead becomes an inequality $p_{c2}+\overline{p}_{c1}<1$. We also find that the critical behavior is well described by the scaling form previously found for regular hyperbolic lattices.

  • 12.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan University, Suwon, Korea.
    Comment on `Six-state clock model on the square lattice: Fisher zeroapproach with Wang-Landau sampling'2010Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 81, nr 6, s. 3101-Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    Hwang in [Phys. Rev. E {\bf{80}}, 042103 (2009)] suggested that the two transitions of the six-state clock model on the square lattice are\emph{not} of the Kosterlitz-Thouless type. Here we show from simulations thatat the upper transition, the helicity modulus does make a discontinuous jumpto zero. This gives strong evidence for a Kosterlitz-Thoulesstransition.

  • 13.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Kosterlitz-Thouless transition of magnetic dipoles on thetwo-dimensional plane2011Inngår i: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 83, nr 18, s. 184409-5 pArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The universality class of a phase transition is often determined by factorslike dimensionality and inherent symmetry. We study the magneticdipole system in which the ground-state symmetry and the underlying latticestructure are coupled to each other in an intricate way. A two-dimensional(2D)square-lattice system of magnetic dipoles undergoes an order-disorder phasetransition belonging to the 2D Ising universality class.According to Prakash and Henley [Phys. Rev. B {\bf 42}, 6572 (1990)], this can berelated to the fourfold-symmetric ground states which suggests a similarityto the four-state clock model. Provided that this type ofsymmetry connection holds true, the magnetic dipoles on a honeycomb lattice,which possess sixfold-symmetric ground states, should exhibit aKosterlitz-Thouless transition in accordance with the six-state clock model.This is verified through numerical simulations in the present investigation.However, it is pointed out that this symmetry argument does not alwaysapply, which suggests that factors other than symmetry can be decisive forthe universality class of the magnetic dipole system.

  • 14.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Department of Physics, BK21 Physics Research Division, Sungkyunkwan University, Suwon 440-746, Korea.
    Percolation in hyperbolic lattices2009Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 79, nr 1, s. 011124-011130Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.

  • 15.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan University, Suwon, Korea.
    Surface and bulk criticality in midpoint percolation2010Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 81, nr 4, s. 1108-6 sidorArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The concept of midpoint percolation has recently been applied tocharacterize the double percolation transitions in negatively curvedstructures. Regular $d$-dimensional hypercubic lattices are in the presentwork investigated using the same concept.Specifically, the site-percolation transitions at the critical thresholds areinvestigated for dimensions up to $d=10$ by means of the Leath algorithm.It is shown that the explicit inclusion of the boundariesprovides a straightforward way to obtain critical indices, both for thebulk and surface parts. At and above the critical dimension $d=6$, it isfound that the percolation cluster contains only a finite number of surfacepoints in the infinite-size limit. This is in accordance with theexpectation from studies of lattices with negative curvature. It is alsofound that the number of surface points, reached by the percolation clusterin the infinite limit, approaches $2d$ for large dimensions $d$. We alsonote that the size dependence in proliferation of percolatingclusters for $d\ge 7$ can be obtained by solely counting surface pointsof the midpoint cluster.

  • 16.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    The Ten Thousand Kims2011Inngår i: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 13, s. 073036-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the Korean culture the family members are recorded in special familybooks. This makes it possible to follow the distribution of Korean familynames far back in history. It is here shown that these name distributionsare well described by a simple null model, the random group formation (RGF)model. This model makes it possible to predict how the name distributionschange and these predictions are shown to be borne out. In particular, theRGF model predicts that, for married women entering a collection of familybooks in a certain year, the occurrence of the most common family name``Kim'' should be directly proportional the total number of married womenwith the same proportionality constant for all the years. This prediction isalso borne out to high degree. We speculate that it reflects some inherentsocial stability in the Korean culture. In addition, we obtain an estimate ofthe total population of the Korean culture down to year 500 AD, based on theRGF model and find about ten thousand Kims.

  • 17.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan University, Korea.
    True and quasi long-range order in the generalized q-state clock model2009Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 80, s. 060101-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    From consideration of the order-parameter distribution,we propose an observable which makes a clear distinction betweentrue and quasi long-range orders in the two-dimensionalgeneralized $q$-state clock model.Measuring this quantity by Monte Carlo simulations for $q=8$, weconstruct a phase diagram and identify critical properties acrossthe phase-separation lines among the true long-range order, quasilong-range order, and disorder. Our result supports the theoreticalprediction that there appears a discontinuous order-disorder transition assoon as the two phase-separation lines merge.

  • 18.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Mäkelä, Harri
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Critical temperatures of the three- and four-state Potts models on the kagome lattice2011Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 83, nr 6, s. 061104-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The value of the internal energy per spin is independent of the strip widthfor a certain class of spin systems on two dimensional infinite strips. Itis verified that the Ising model on the kagome lattice belongs to this classthrough an exact transfer-matrix calculation of the internal energy for thetwo smallest widths. More generally, one can suggest an upper bound forthe critical coupling strength $K_c(q)$ for the $q$-state Potts model fromexact calculations of the internal energy for the two smallest stripwidths. Combining this with the corresponding calculation for the duallattice and using an exact duality relation enables us to conjecture thecritical coupling strengths for the three- and four-state Pottsmodels on the kagome lattice. The values are $K_c(q=3)=1.056~509~426~929~0$and $K_c(q=4) = 1.149~360~587~229~2$,and the values can, in principle, be obtained to an arbitrary precision. Wediscuss the fact that these values are in the middle of earlierapproximate results and furthermore differ from earlier conjecturesfor the exact values.

  • 19.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Mäkelä, Harri
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Ising model on a hyperbolic plane with a boundary2011Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, s. 032103-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A hyperbolic plane can be modeled by a structure called the enhanced binarytree. We study the ferromagnetic Ising model on top of the enhanced binarytree using the renormalization-group analysis in combination withtransfer-matrix calculations. We find a reasonable agreement with MonteCarlo calculations on the transition point, and the resulting criticalexponents suggest the mean-field surface critical behavior.

  • 20.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Shima, Hiroyuki
    Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan.
    Kim, Beom Jun
    BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea.
    Curvature-induced frustration in the XY model on hyperbolic surfaces2009Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 79, nr 6, s. 060106(R)-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study low-temperature properties of the XY spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters scattered over the system. Asymptotic behavior of the spin-glass susceptibility suggests a zero-temperature glass transition, which is attributed to multiple optimal configurations of spin clusters due to nonzero surface curvature of the system. It implies that a constant ferromagnetic spin interaction on a regular lattice can exhibit glasslike behavior without possessing any disorder if the lattice is put on top of a negatively curved space such as a hyperbolic surface.

  • 21.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Um, Jaegon
    Korea Institute for Advanced Study, Seoul, Korea.
    Yi, Su Do
    Department of Physics, Sungkyunkwan University, Suwon, Republic of Korea.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon, Republic of Korea.
    Quantum Monte Carlo study of the transverse-field quantum Ising modelon infinite-dimensional structures2011Inngår i: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 84, s. 174419-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In a number of classical statistical-physical models, there exists acharacteristic dimensionality called the upper critical dimension abovewhich one observes the mean-field critical behavior. Instead of constructinghigh-dimensional lattices, however, one can also considerinfinite-dimensional structures, and the question is whether this mean-fieldcharacter extends to quantum-mechanical cases as well. We thereforeinvestigate the transverse-field quantum Ising model on the globally couplednetwork and on the Watts-Strogatz small-world network by means of quantum MonteCarlo simulations and the finite-size scaling analysis. We confirm that bothof the structures exhibit critical behavior consistent with the mean-fielddescription. In particular, we show that the existing cumulant methodhas difficulty in estimating the correct dynamic critical exponent andsuggest that an order parameter based on the quantum-mechanicalexpectation value can be a practically useful numerical observable todetermine critical behavior when there is no well-defined dimensionality.

  • 22.
    Bernhardsson, Sebastian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Baek, Seung Ki
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    A Paradoxical Property of the Monkey Book2011Inngår i: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, s. P07013-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A 'monkey book' is a book consisting of a random sequence of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book to real books. It is shown that the word distribution statistics for the monkey book is different and quite distinct from a typical real book. In particular, the monkey book obeys Heaps' power law to an extraordinarily good approximation, in contrast to the word distributions for real books, which deviate from Heaps' law in a characteristic way. This discrepancy is traced to the different properties of a 'spiked' distribution and its smooth envelope. The somewhat counter-intuitive conclusion is that a 'monkey book' obeys Heaps' power law precisely because its word-frequency distribution is not a smooth power law, contrary to the expectation based on simple mathematical arguments that if one is a power law, so is the other.

  • 23.
    Bokma, Folmer
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Baek, Seung Ki
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    50 years of inordinate fondness2014Inngår i: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 63, nr 2, s. 251-256Artikkel i tidsskrift (Fagfellevurdert)
  • 24.
    Minnhagen, Petter
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Baek, Seung Ki
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Analytic results for the percolation transitions of the enhancedbinary tree2010Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 82, s. 011113-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Percolation for a planar lattice has a single percolation threshold, whereaspercolation for a negatively curved lattice displays two separate thresholds.The enhanced binary tree (EBT) can be viewed as aprototype model displaying two separate percolation thresholds.We present an analytic result for the EBT model which givestwo critical percolation threshold probabilities,$p_{c1}=\frac{1}{2}\sqrt{13}-\frac{3}{2}$ and $p_{c2}=1/2$,and yields a size-scaling exponent $\Phi =\ln\left[\frac{p(1+p)}{1-p(1-p)}\right]/\ln 2$. It is inferred that the twothresholdvalues give exact upper limits and that $p_{c1}$ is furthermore exact. Inaddition, we argue that $p_{c2}$ is also exact. The physics of the model andthe results are described within themidpoint-percolation concept: Monte Carlo simulations are presented for thenumber of boundary points which are reached from the midpoint, and theresults are compared to the number of routes from the midpoint to theboundary given by the analytic solution. These comparisonsprovide a more precise physical picture of what happens at the transitions.Finally, the results are compared to related works, in particular, the Cayleytree and Monte Carlo results for hyperbolic lattices as well as earlierresults for the EBT model. It disproves a conjecture that the EBT has anexact relation to the thresholds of its dual lattice.

  • 25.
    Seung Ki, Baek
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Minnhagen, Petter
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Shima, Hiroyuki
    Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan.
    Kim, Beom Jun
    BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea.
    Phase transition of q-state clock models on heptagonal lattices2009Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 80, nr 1, s. 011133-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the q-state clock models on heptagonal lattices assigned on a negatively curved surface. We show that the system exhibits three classes of equilibrium phases; in between ordered and disordered phases, an intermediate phase characterized by a diverging susceptibility with no magnetic order is observed at every q ≥ 2. The persistence of the third phase for all q is in contrast with the disappearance of the counterpart phase in a planar system for small q, which indicates the significance of nonvanishing surface-volume ratio that is peculiar in the heptagonal lattice. Analytic arguments based on Ginzburg-Landau theory and generalized Cayley trees make clear that the two-stage transition in the present system is attributed to an energy gap of spin-wave excitations and strong boundary-spin contributions. We further demonstrate that boundary effects breaks the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.

1 - 25 of 25
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