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Lundow, Per-Håkan

Open this publication in new window or tab >>Hyperscaling Violation in Ising Spin Glasses### Campbell, Ian A.

### Lundow, Per-Håkan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 10, article id 978Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

MDPI, 2019
##### Keywords

spin glasses, random interactions, scaling, hyperscaling
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-165329 (URN)10.3390/e21100978 (DOI)000495094000060 ()
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Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2019-12-02Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D=6. Estimates are obtained for the "violation of hyperscaling exponent" values in the various models.

Open this publication in new window or tab >>Revisiting the cavity-method threshold for random 3-SAT### Lundow, Per-Håkan

### Markström, Klas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 99, no 2, article id 022106Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Physical Society, 2019
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-162509 (URN)10.1103/PhysRevE.99.022106 (DOI)000458140700001 ()30934345 (PubMedID)
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Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-08-21Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies α_{3}≤4.262. If the assumption is correct, this means that the actual threshold value for *k*=3 is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large *k*. Our result thus indicate that there are distinct behaviors for *k* above and below some critical *k _{c}*, and the cavity method may provide a correct mean-field picture for the range above

Open this publication in new window or tab >>A counterexample to a conjecture by Blocki-Zwonek### Åhag, Per

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Czyz, Rafal

### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 27, no 1, p. 119-124Article in journal (Refereed) Published
##### Place, publisher, year, edition, pages

Philadelphia: Taylor & Francis, 2018
##### Keywords

Błocki–Zwonek conjectures, Bergman kernel, Green functions, Jacobi functions
##### National Category

Mathematical Analysis Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-125362 (URN)10.1080/10586458.2016.1230913 (DOI)
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Available from: 2016-09-09 Created: 2016-09-09 Last updated: 2018-06-07Bibliographically approved

Open this publication in new window or tab >>Bimodal Ising spin glass in two dimensions: the anomalous dimension η### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 2, article id 024203Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Physical Society, 2018
##### National Category

Other Physics Topics
##### Identifiers

urn:nbn:se:umu:diva-144836 (URN)10.1103/PhysRevB.97.024203 (DOI)000423340800006 ()
#####

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Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2018-06-09Bibliographically approved

Direct measurements of the spin glass correlation function G(R) for Gaussian and bimodal Ising spin glasses in dimension two have been carried out in the temperature region T ∼ 1. In the Gaussian case the data are consistent with the known anomalous dimension value η ≡ 0. For the bimodal spin glass in this temperature region T > T*(L), well above the crossover T*(L) to the ground-state-dominated regime, the effective exponent η is clearly nonzero and the data are consistent with the estimate η ∼ 0.28(4) given by McMillan in 1983 from similar measurements. Measurements of the temperature dependence of the Binder cumulant U_{4}(T, L) and the normalized correlation length ξ(T, L)/L for the two models confirms the conclusion that the two-dimensional (2D) bimodal model has a nonzero effective η both below and above T*(L). The 2D bimodal and Gaussian interaction distribution Ising spin glasses are not in the same universality class.

Open this publication in new window or tab >>Hyperscaling breakdown and Ising spin glasses: The Binder cumulant### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 492, p. 1838-1852Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018
##### Keywords

Spin glasses, Ising model, Hyperscaling
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-145133 (URN)10.1016/j.physa.2017.11.101 (DOI)000423495100151 ()
#####

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Available from: 2018-03-05 Created: 2018-03-05 Last updated: 2018-06-09Bibliographically approved

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.

Open this publication in new window or tab >>The Ising universality class in dimension three: Corrections to scaling### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 511, p. 40-53Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018
##### Keywords

3D Ising model, Scaling, Corrections to scaling
##### National Category

Other Physics Topics Condensed Matter Physics Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-152237 (URN)10.1016/j.physa.2018.06.087 (DOI)000444667800004 ()
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Available from: 2018-10-04 Created: 2018-10-04 Last updated: 2018-10-04Bibliographically approved

Simulation data are analyzed for four 3D spin-1/2 Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and the normalized Binder cumulant. From measurements covering the entire paramagnetic temperature regime the corrections to scaling are estimated. We conclude that a correction term having an exponent which is consistent within the statistics with the bootstrap value of the universal subleading thermal confluent correction exponent, theta(2) similar to 2.454(3), is almost always present with a significant amplitude. In all four models, for the normalized Binder cumulant the leading confluent correction term has zero amplitude. This implies that the universal ratio of leading confluent correction amplitudes a(x4)/a(x) = 2 in the 3D Ising universality class.

Open this publication in new window or tab >>Ising spin glasses in dimension five### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Physical Review E, ISSN 2470-0045, Vol. 95, no 1, article id 012112Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-132030 (URN)10.1103/PhysRevE.95.012112 (DOI)000391864200001 ()
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Available from: 2017-03-28 Created: 2017-03-28 Last updated: 2018-06-09Bibliographically approved

Ising spin-glass models with bimodal, Gaussian, uniform, and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the thermodynamic limit regime. It is shown that the values of critical exponents and of dimensionless observables at criticality are model dependent. Models in a single universality class have identical values for each of these critical parameters, so Ising spin-glass models in dimension five with different interaction distributions each lie in different universality classes. This result confirms conclusions drawn from measurements in dimension four and dimension two.

Open this publication in new window or tab >>Ising spin glasses in two dimensions: Universality and nonuniversality### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 4, article id 042107Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-134727 (URN)10.1103/PhysRevE.95.042107 (DOI)000399393000003 ()
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Available from: 2017-05-19 Created: 2017-05-19 Last updated: 2018-06-09Bibliographically approved

Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising spin glass (ISG) models in two dimensions [Lundow and Campbell, Phys. Rev. E 93, 022119 (2016)]. Here we further analyze the bimodal and Gaussian data together with data on two other continuous interaction distribution two-dimensional ISG models, the uniform and the Laplacian models, and three other discrete interaction distribution models, a diluted bimodal model, an "antidiluted" model, and a more exotic symmetric Poisson model. Comparisons between the three continuous distribution models show that not only do they share the same exponent eta equivalent to 0 but that to within the present numerical precision they share the same critical exponent. also, and so lie in a single universality class. On the other hand the critical exponents of the four discrete distribution models are not the same as those of the continuous distributions, and the present data strongly indicate that they differ from one discrete distribution model to another. This is evidence that discrete distribution ISG models in two dimensions have nonzero values of the critical exponent. and do not lie in a single universality class.

Open this publication in new window or tab >>Bimodal and Gaussian Ising spin glasses in dimension two### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Physical Review E, ISSN 2470-0045, Vol. 93, no 2, article id 022119Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:umu:diva-117818 (URN)10.1103/PhysRevE.93.022119 (DOI)000370029400002 ()
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Available from: 2016-04-07 Created: 2016-03-04 Last updated: 2018-06-07Bibliographically approved

An analysis is given of numerical simulation data to size L = 128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (+/- J) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent. = 0, and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T *(L) there is a regime of effectively continuous energy levels; below T *(L) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T *(L) tends to zero at very large L, leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t = T and with a scaling variable tau(b) = T-2 /(1 + T 2) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility x(tau(b), L) and second moment correlation length xi(tau(b), L) in the thermodynamic limit regime are extrapolated to the tau(b) = 0 critical limit. The Gaussian critical exponent estimates from the simulations, eta= 0 and nu= 3.55(5), are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are eta= 0.20(2) and nu= 4.8(3), distinctly different from the Gaussian critical exponents.

Open this publication in new window or tab >>Non-self-averaging in Ising spin glasses and hyperuniversality### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

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##### Abstract [en]

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Mathematical Analysis, Physics
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:umu:diva-116080 (URN)10.1103/PhysRevE.93.012118 (DOI)000367901000011 ()
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Available from: 2016-02-10 Created: 2016-02-08 Last updated: 2018-06-07Bibliographically approved

Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample variance) parameter U-22(T, L) for the spin glass susceptibility [and for higher moments Unn (T, L)] is reported for dimensions 2,3,4,5, and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length xi(T, L) as U-nn(beta, L) = [K-d xi (T, L)/L](d) and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Empirically, it is found that the Kd values are independent of d to within the statistics. The maximum values [U-nn(T, L)](max) are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [U-nn (T, L)](max) peak values are also practically dimension-independent to within the statistics and so are " hyperuniversal." These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for three-dimensional Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario.