Equilibrium Phase Transitions in Statistical Physics

2019 ◽  
pp. 129-278
Author(s):  
Tian Ma ◽  
Shouhong Wang
Keyword(s):  
Phase Transitions ◽  
Statistical Physics ◽  
Equilibrium Phase

scholarly journals Machine learning of phase transitions in nonlinear polariton lattices

2022 ◽  
Vol 5 (1) ◽  
Author(s):  
Daria Zvyagintseva ◽  
Helgi Sigurdsson ◽  
Valerii K. Kozin ◽  
Ivan Iorsh ◽  
Ivan A. Shelykh ◽  
...  
Keyword(s):  
Machine Learning ◽  
Phase Transitions ◽  
Steady State ◽  
Statistical Physics ◽  
Equilibrium Phase ◽  
Nearest Neighbour ◽  
System Parameters ◽  
Machine Learning Methods ◽  
Unsupervised Data Mining ◽  
Qualitative Changes

AbstractPolaritonic lattices offer a unique testbed for studying nonlinear driven-dissipative physics. They show qualitative changes of their steady state as a function of system parameters, which resemble non-equilibrium phase transitions. Unlike their equilibrium counterparts, these transitions cannot be characterised by conventional statistical physics methods. Here, we study a lattice of square-arranged polariton condensates with nearest-neighbour coupling, and simulate the polarisation (pseudospin) dynamics of the polariton lattice, observing regions with distinct steady-state polarisation patterns. We classify these patterns using machine learning methods and determine the boundaries separating different regions. First, we use unsupervised data mining techniques to sketch the boundaries of phase transitions. We then apply learning by confusion, a neural network-based method for learning labels in a dataset, and extract the polaritonic phase diagram. Our work takes a step towards AI-enabled studies of polaritonic systems.

scholarly journals TELESCOPIC LINKAGES AND A TOPOLOGICAL APPROACH TO PHASE TRANSITIONS

2011 ◽  
Vol 90 (2) ◽  
pp. 183-195 ◽  
Author(s):  
MICHAEL FARBER ◽  
VIKTOR FROMM
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Configuration Space ◽  
Betti Number ◽  
Statistical Physics ◽  
Betti Numbers ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Exponential Growth Rate ◽  
Topological Approach

AbstractA topological approach to the theory of equilibrium phase transitions in statistical physics is based on the topological hypothesis, which claims that phase transitions are due to changes of the topology of suitable submanifolds in the configuration space. In this paper we examine in detail the antiferromagnetic mean-field XY model and study the topology of the subenergy manifolds. The latter can be interpreted mechanically as the configuration space of a linkage with one telescopic leg. We use methods of Morse theory to describe explicitly the Betti numbers of this configuration space. We apply these results to the antiferromagnetic mean-field XY model and compute the exponential growth rate of the total Betti number. Previous authors studied the Euler characteristic rather than the total Betti number. We show that in the presence of an external magnetic field the model undergoes a single ‘total Betti number phase transition’.

Statistical physics and phase transitions

2012 ◽  
pp. 12-42
Author(s):  
Lorenza Saitta ◽  
Attilio Giordana ◽  
Antoine Cornuejols
Keyword(s):  
Phase Transitions ◽  
Statistical Physics

scholarly journals Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200688
Author(s):  
Valerio Lucarini ◽  
Grigorios A. Pavliotis ◽  
Niccolò Zagli
Keyword(s):  
Phase Transitions ◽  
Thermodynamic Limit ◽  
Linear Response ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Transitions ◽  
Autocorrelation Time ◽  
The Common ◽  
Fokker Planck Equations ◽  
Non Equilibrium

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

scholarly journals Crystallization of Binary Alloys and Non-Equilibrium Phase Transitions

2019 ◽  
Vol 489 (6) ◽  
pp. 545-551
Author(s):  
E. V. Radkevich ◽  
O. A. Vasil’eva ◽  
M. I. Sidorov
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Numerical Experiments ◽  
Binary Alloys ◽  
Equilibrium Phase ◽  
Homogeneous State ◽  
Nonequilibrium Phase Transition ◽  
Nonequilibrium Phase ◽  
Initial Stage ◽  
Melt Cooling

A model was constructed for the reconstruction of the initial stage of crystallization of binary alloys as a nonequilibrium phase transition, the mechanism of which is diffusion stratification. Numerical experiments were performed. Self-excitation of a homogeneous state by the edge control melt cooling condition.

scholarly journals Mixed-order phase transition in a colloidal crystal

2017 ◽  
Vol 114 (49) ◽  
pp. 12906-12909 ◽  
Author(s):  
Ricard Alert ◽  
Pietro Tierno ◽  
Jaume Casademunt
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Colloidal Particles ◽  
Colloidal Crystal ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Dimension ◽  
Colloidal System ◽  
Test Bed ◽  
Mixed Order

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid–solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field H. At the transition field Hs, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length ξ∝|H2−Hs2|−1/2. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is du=2. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

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