Special Issue "Phase Transitions and Critical Phenomena in Frustrated Systems and Thin Films"

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

Deadline for manuscript submissions: closed (20 December 2018).

Special Issue Editor

Prof. Dr. Hung T. Diep
E-Mail Website
Guest Editor
Laboratoire de Physique Théorique et Modélisation Université de Cergy-Pontoise, CNRS, UMR 8089 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
Interests: theoretical physics with focus on critical phenomena and phase transitions
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Special Issue Information

Dear Colleagues,

Phase transitions and critical phenomena occupy the central place of statistical physics. These subjects have important applications in materials science and in other sciences. Why are such studies interesting for so many disciplines? One of the answers resides in the fact that, if we know characteristics of a phase transition, we can understand interaction mechanisms between constituents composing the material. Beyond fundamental interests, understanding these mechanisms allows us to artificially modify the material to get a desired property. 

The theory of phase transitions made remarkable advances in the 1970s with the concept of the renormalization group (RG), introduced by K.H. Wilson. RG provides a clear physical picture about how a collective excitation of particles in a system can induce a change of its symmetry. RG has successfully explained the nature of the phase transitions and the critical properties of many systems, in agreement with experiments.  However, the application of RG in complicated systems, such as systems with competing interactions, is not simple; let alone its questionable validity due to various approximations used.

The purpose of this Special Issue is to give an opportunity to publish papers on phase transitions and criticality in complex systems, such as frustrated systems, low-dimensional quantum spin systems, and thin films. We welcome overviews and surveys on rapidly-developed domains, and original papers using theory, simulations, and experiments.

Prof. Dr. Hung T. Diep
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 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 in Complex Systems
  • Criticality
  • Monte Carlo Simulation
  • Frustrated Spin Systems
  • Quantum Phase Transition
  • Low-Dimensional Quantum Spin Systems
  • Phase Transition in Disordered Systems
  • Phase Transition in Thin Films

Published Papers (5 papers)

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Research

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Open AccessArticle
Two-Dimensional Electronic Transport in Rubrene: The Impact of Inter-Chain Coupling
Entropy 2019, 21(3), 233; https://doi.org/10.3390/e21030233 - 28 Feb 2019
Cited by 1 | Viewed by 1310
Abstract
Organic semi-conductors have unique electronic properties and are important systems both at the fundamental level and also for their applications in electronic devices. In this article we focus on the particular case of rubrene which has one of the best electronic transport properties [...] Read more.
Organic semi-conductors have unique electronic properties and are important systems both at the fundamental level and also for their applications in electronic devices. In this article we focus on the particular case of rubrene which has one of the best electronic transport properties for application purposes. We show that this system can be well simulated by simple tight-binding systems representing one-dimensional (1D) chains that are weakly coupled to their neighboring chains in the same plane. This makes in principle this rubrene system somehow intermediate between 1D and isotropic 2D models. We analyse in detail the dc-transport and terahertz conductivity in the 1D and in the anisotropic 2D models. The transient localisation scenario allows us to reproduce satisfactorily some basics results such as mobility anisotropy and orders of magnitude as well as ac-conductivity in the terahertz range. This model shows in particular that even a weak inter-chain coupling is able to improve notably the propagation along the chains. This suggest also that a strong inter-chain coupling is important to get organic semi-conductors with the best possible transport properties for applicative purposes. Full article
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Open AccessArticle
Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model
Entropy 2019, 21(2), 153; https://doi.org/10.3390/e21020153 - 05 Feb 2019
Viewed by 1372
Abstract
The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used [...] Read more.
The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros. Full article
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Open AccessArticle
Entropy Driven Phase Transition in Polymer Gels: Mean Field Theory
Entropy 2018, 20(7), 501; https://doi.org/10.3390/e20070501 - 30 Jun 2018
Cited by 3 | Viewed by 1637
Abstract
We present a mean field model of a gel consisting of P polymers, each of length L and Nz polyfunctional monomers. Each polyfunctional monomer forms z covalent bonds with the 2P bifunctional monomers at the ends of the linear polymers. We [...] Read more.
We present a mean field model of a gel consisting of P polymers, each of length L and Nz polyfunctional monomers. Each polyfunctional monomer forms z covalent bonds with the 2P bifunctional monomers at the ends of the linear polymers. We find that the entropy dependence on the number of polyfunctional monomers exhibits an abrupt change at Nz = 2P/z due to the saturation of possible crosslinks. This non-analytical dependence of entropy on the number of polyfunctionals generates a first-order phase transition between two gel phases: one poor and the other rich in poly-functional molecules. Full article
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Review

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Open AccessFeature PaperReview
From Spin Glasses to Negative-Weight Percolation
Entropy 2019, 21(2), 193; https://doi.org/10.3390/e21020193 - 18 Feb 2019
Viewed by 1102
Abstract
Spin glasses are prototypical random systems modelling magnetic alloys. One important way to investigate spin glass models is to study domain walls. For two dimensions, this can be algorithmically understood as the calculation of a shortest path, which allows for negative distances or [...] Read more.
Spin glasses are prototypical random systems modelling magnetic alloys. One important way to investigate spin glass models is to study domain walls. For two dimensions, this can be algorithmically understood as the calculation of a shortest path, which allows for negative distances or weights. This led to the creation of the negative weight percolation (NWP) model, which is presented here along with all necessary basics from spin glasses, graph theory and corresponding algorithms. The algorithmic approach involves a mapping to the classical matching problem for graphs. In addition, a summary of results is given, which were obtained during the past decade. This includes the study of percolation transitions in dimension from d = 2 up to and beyond the upper critical dimension d u = 6 , also for random graphs. It is shown that NWP is in a different universality class than standard percolation. Furthermore, the question of whether NWP exhibits properties of Stochastic–Loewner Evolution is addressed and recent results for directed NWP are presented. Full article
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Open AccessReview
Phase Transition in Frustrated Magnetic Thin Film—Physics at Phase Boundaries
Entropy 2019, 21(2), 175; https://doi.org/10.3390/e21020175 - 13 Feb 2019
Cited by 6 | Viewed by 1355
Abstract
In this review, we outline some principal theoretical knowledge of the properties of frustrated spin systems and magnetic thin films. The two points we would like to emphasize: (i) the physics in low dimensions where exact solutions can be obtained; (ii) the physics [...] Read more.
In this review, we outline some principal theoretical knowledge of the properties of frustrated spin systems and magnetic thin films. The two points we would like to emphasize: (i) the physics in low dimensions where exact solutions can be obtained; (ii) the physics at phase boundaries where interesting phenomena can occur due to competing interactions of the two phases around the boundary. This competition causes a frustration. We will concentrate our attention on magnetic thin films and phenomena occurring near the boundary of two phases of different symmetries. Two-dimensional (2D) systems are in fact the limiting case of thin films with a monolayer. Naturally, we will treat this case at the beginning. We begin by defining the frustration and giving examples of frustrated 2D Ising systems that we can exactly solve by transforming them into vertex models. We will show that these simple systems already contain most of the striking features of frustrated systems such as the high degeneracy of the ground state (GS), many phases in the GS phase diagram in the space of interaction parameters, the reentrance occurring near the boundaries of these phases, the disorder lines in the paramagnetic phase, and the partial disorder coexisting with the order at equilibrium. Thin films are then presented with different aspects: surface elementary excitations (surface spin waves), surface phase transition, and criticality. Several examples are shown and discussed. New results on skyrmions in thin films and superlattices are also displayed. By the examples presented in this review we show that the frustration when combined with the surface effect in low dimensions gives rise to striking phenomena observed in particular near the phase boundaries. Full article
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