Special Issue "Phase Transitions and Emergent Phenomena: How Change Emerges through Basic Probability Models"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 30 December 2019.

Special Issue Editor

Prof. Ralph Kenna
E-Mail Website
Guest Editor
Statistical Physics Group, Centre for Fluid and Complex Systems, Coventry University CV1 5FB, UK
Interests: phase transitions; critical phenomena; exact solutions; finite size scaling; partition-function zeros; renormalization group; logarithmic corrections; scaling relations; universality; complex systems; sociophysics; networks; digital humanities

Special Issue Information

Dear Colleagues,

Ludwig Boltzmann and contemporaries pioneered the development of statistical physics towards the end of the 19th century. The pillars on which the discipline rests include “bottom-up” theories of phase transitions and critical phenomena, built on other pioneering ideas and work such as that of Wilhelm Lenz and Ernst Ising at the start of the 20th century. In the words of Stephen Hawking, we are now in the “century of complexity”, moving on from basic laws that govern matter to how everything is connected to everything else.

Although Ising’s original investigations did not deliver the desired result of a phase transition, the idea that randomness coupled with gross simplification at the micro-level could explain changes of state at the macro-level was ground-breaking. Now we know the importance of dimensionality; interaction range; symmetries; whether the model is classical or quantum, equilibrium, or non-equilibrium, etc., in understanding the physics of change.

A vast body of research covers how all sorts of variants on such systems describe increasingly complex systems, but the essential idea to apply probabilistic considerations to simplified many-body systems was borrowed from socio systems. In recent times, with the emergence of the notion of “emergence”, the statistical physics of complex systems has re-embraced its interdisciplinary birthplace, delivering rich physics in and beyond physics and contributing to our understanding of the world.

This Special Issue focuses on models that are simplified at the micro level but complex at the macro level. We are interested in negative results like Ising’s as well as positive results, and, reflecting the birthplace of statistical physics, we welcome interdisciplinary considerations as well as traditional physics. Thus, this Issue focuses on the concept of change—how the simple can deliver the complex through non-trivial mechanisms, wherever they arise.

This special issue is dedicated to the fond memory of Professor Ian Campbell who has contributed so much to our understanding of phase transitions and emergent phenomena. In particular, Ian’s discovery of extended scaling, and his research into hyperscaling and spin glasses have contributed very significantly to theories of critical phenomena and we anticipate they will contribute more in the years to come. We are honored that Ian’s last paper (co-authored with Per-Håkan Lundow) is published in this special issue.

 

Prof. Dr. Ralph Kenna
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Phase transitions
  • Critical phenomena
  • Universality
  • Scaling
  • Statistical physics concepts applied to other disciplines

Published Papers (3 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Open AccessArticle
Hyperscaling Violation in Ising Spin Glasses
Entropy 2019, 21(10), 978; https://doi.org/10.3390/e21100978 - 08 Oct 2019
Abstract
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 [...] Read more.
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. Full article
Show Figures

Figure 1

Open AccessArticle
Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks
Entropy 2019, 21(10), 942; https://doi.org/10.3390/e21100942 - 26 Sep 2019
Abstract
Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity [...] Read more.
Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class. Full article
Show Figures

Figure 1

Open AccessFeature PaperArticle
Universality and Exact Finite-Size Corrections for Spanning Trees on Cobweb and Fan Networks
Entropy 2019, 21(9), 895; https://doi.org/10.3390/e21090895 - 15 Sep 2019
Abstract
The concept of universality is a cornerstone of theories of critical phenomena. It is very well understood in most systems, especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the edge and corner contributions to free [...] Read more.
The concept of universality is a cornerstone of theories of critical phenomena. It is very well understood in most systems, especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the edge and corner contributions to free energies and response functions is less investigated and less well understood. In particular, the question arises of how universality is maintained in correction-to-scaling in systems of the same universality class but with very different corner geometries. Two-dimensional geometries deliver the simplest such examples that can be constructed with and without corners. To investigate how the presence and absence of corners manifest universality, we analyze the spanning tree generating function on two different finite systems, namely the cobweb and fan networks. The corner free energies of these configurations have stimulated significant interest precisely because of expectations regarding their universal properties and we address how this can be delivered given that the finite-size cobweb has no corners while the fan has four. To answer, we appeal to the Ivashkevich–Izmailian–Hu approach which unifies the generating functions of distinct networks in terms of a single partition function with twisted boundary conditions. This unified approach shows that the contributions to the individual corner free energies of the fan network sum to zero so that it precisely matches that of the web. It therefore also matches conformal theory (in which the central charge is found to be c = 2 ) and finite-size scaling predictions. Correspondence in each case with results established by alternative means for both networks verifies the soundness of the Ivashkevich–Izmailian–Hu algorithm. Its broad range of usefulness is demonstrated by its application to hitherto unsolved problems—namely the exact asymptotic expansions of the logarithms of the generating functions and the conformal partition functions for fan and cobweb geometries. We also investigate strip geometries, again confirming the predictions of conformal field theory. Thus, the resolution of a universality puzzle demonstrates the power of the algorithm and opens up new applications in the future. Full article
Show Figures

Figure 1

Back to TopTop