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Dynamic critical behavior of the XY model in small-world networks
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Department of Molecular Science and Technology, Ajou University, Suwon 442-749, Korea.
2003 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 67, no 3, 036118- p.Article in journal (Refereed) Published
Abstract [en]

The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for P≳0.03.

Place, publisher, year, edition, pages
American Physical Society , 2003. Vol. 67, no 3, 036118- p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-2145DOI: 10.1103/PhysRevE.67.036118OAI: oai:DiVA.org:umu-2145DiVA: diva2:139986
Available from: 2003-09-15 Created: 2003-09-15 Last updated: 2012-06-12Bibliographically approved
In thesis
1. Characteristic properties of two-dimensional superconductors close to the phase transition in zero magnetic field
Open this publication in new window or tab >>Characteristic properties of two-dimensional superconductors close to the phase transition in zero magnetic field
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The main focus of this thesis lies on the critical properties of twodimensional (2D) superconductors in zero magnetic field. Simulations based on variants of the 2D XY model are shown to give characteristic features close to the phase transition which agree qualitatively with experimental data. Thus, it is concluded that these common characteristic features are caused by two-dimensional vortices.

The thesis consists of an introductory part and five separate publications. In the introductory part of the thesis the basic results of the Ginzburg-Landau model, which gives a phenomenological description of superconductors, are described. In 2D systems, the superconductive phase transition in the absence of a magnetic field is governed by the unbinding of thermally created vortices and is called the Kosterlitz-Thouless (KT) phase transition. An introduction to this kind of transition is given. The important features of the current-voltage (IV) characteristics and the nonlinear conductivity, which can be used to study the KT transition, are discussed. The scaling analysis procedure, a powerful tool for the analysis of the properties of a system in the vicinity of phase transition, is reviewed. A scaling form for the nonlinear dc conductivity, which takes into account finite-size e ects, is discussed.

The static 2D XY model, which is usually used to describe superfluids, superconducting films as well as the high-Tc superconductors with high anisotropy, is introduced. Three different types of dynamic models, namely resistively shunted junction, relaxational, and Monte Carlo dynamics are superimposed on the 2D XY model for the evaluation of the dynamic properties. TheVillain model and a modifiedXY model using a p-type interaction potential exhibit different densities of the thermally created vortices. Since the dominant characteristic physical features close to the KT transition are associated with vortex pair fluctuations these two models are investigated.

The introductory part closes with a short introduction to each of the five published articles.

Publisher
62 p.
Keyword
Physics, Fysik, superconductor, two dimensions, phase transition, vortex, currentvoltage characteristics, complex conductivity, scaling, critical exponents, XY-type models, dynamics
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-102 (URN)91-7305-490-9 (ISBN)
Public defence
2003-10-03, Umeå, 10:00
Available from: 2003-09-15 Created: 2003-09-15Bibliographically approved
2. Form and function of complex networks
Open this publication in new window or tab >>Form and function of complex networks
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Form och funktion i komplexa nätverk
Abstract [en]

Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2004. 104 p.
Keyword
Theoretical physics, complex networks, complexity, small-world networks, scale-free networks, graph theory, Teoretisk fysik
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-222 (URN)91-7305-629-4 (ISBN)
Public defence
2004-05-07, N430, Naturvetarhuset, Umeå Universitet, Umeå, 14:00
Opponent
Supervisors
Available from: 2004-03-26 Created: 2004-03-26 Last updated: 2013-09-06Bibliographically approved

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Minnhagen, Petter

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