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AI for Condensed Matter Physics
Published in Volker Knecht, AI for Physics, 2023
Álvaro Díaz Fernández, Chao Fang, Volker Knecht
As the temperature is increased further, there comes a point where the pairs unbind and isolated vortices and antivortices roam around the system which becomes a disordered plasma of vortices and antivortices. The change from bound to unbound pairs was later called Kosterlitz–Thouless transition. It is a topological phase transition because it is a transition from a disordered phase – although one with quasi-long-range order – to another disordered phase, driven by topological defects. Therefore, there is no violation of the Mermin–Wagner theorem and there is indeed a phase transition, although one not fitting into Landau's scheme. The Nobel Prize in Physics 2016 was awarded in part to Kosterlitz and Thouless for this discovery. The other part of the prize awarded to Thouless and Haldane concerns topological phases of matter, which we shall not touch upon here. The Kosterlitz–Thouless transition has been experimentally observed in several systems including the thin films of helium-4 and the melting of two-dimensional solids.
Basic Physical Concepts of Organic Conductors
Published in Jean-Pierre Farges, Organic Conductors, 2022
where J is a measure of the microscopic interaction energy scale and L is the length of the system. The logarithmic dependence is typical of vortices. One can estimate the entropy of a free vortex to be S ≈ ln[(L/a)2], since there are (L/a)2 different nonoverlapping possible positions for it. Vortices will exist in great numbers (a free-vortex gas phase) when their creation energy Ev is overcome by the gain in entropy S. This occurs for q = 1 at temperatures above TK = Ev/S ≈ πJ/2, the Kosterlitz-Thouless transition temperature. Below this temperature, vortices will bind in opposite-windingnumber pairs with algebraically decaying pair correlations (quasi-LRO). This fluid is permeated with the LRO-destroying phase fluctuations of Section II.
Theory of Phase Transitions and Critical Phenomena
Published in Hung T. Diep, Physics of Magnetic Thin Films, 2021
All systems do not have obligatorily a phase transition. In general, the existence of a phase transition depends on a few general parameters such as the space dimension, the nature of the interaction between particles and the system symmetry. For spin systems, one can give a brief summary here. In one dimension, in general there is no phase transition at a non-zero temperature for systems of short-range interactions regardless of the spin model. The long-range ordering at T = 0 is destroyed as soon as T ≠ 0. However, in two dimensions discrete spin models such as the Ising and Potts models have a phase transition at a finite temperature Tc, while continuous spin models such as the Heisenberg model do not have a transition at a finite temperature [231]. The XY spin model in two dimensions is a very particular case: In spite of the absence of a long-range order at finite temperatures, there is a phase transition of a special kind called the “Kosterlitz–Thouless” transition [191]. In three dimensions, all known spin models have in general a phase transition at Tc ≠ 0. Note that this summary is for non-frustrated systems. Frustrated spin systems have to be separately considered, they often do not follow these observations (see reviews in Ref. [85]).
Dynamics of smectic-C liquid crystals in a stochastic magnetic field
Published in Philosophical Magazine, 2021
The purpose of the present work is to study the dynamic evolution of SmC liquid crystals in the presence of magnetic field. Here we study the stochastic fluctuations on SmC liquid crystals in the presence of magnetic field by dynamic renormalisation group (DRG) approach. Our dynamical model predicts the onset of a Kosterlitz-Thouless transition at low frequency limit. Further our results show that nonlinearity drives the system to a KPZ fixed point. Our approach will be similar to the previous studies by Chattopadhyay [19] and Chattopadhyay and Mukherjee [11, 12].