Phase transition in a nonequilibrium 2D degenerate system

Zhizhen Chen, Zi Cai

Abstract We propose a periodically driven system whose dimensionality is an emergent property that can be tunable, thus enables us to realize not only many-body phases with arbitrary dimensions, but also phase transitions, instead of crossovers, between phases with various dimensions. We study an interacting rotor model whose instantaneous Hamiltonian keeps the one-dimensional feature at any given time. Despite this, an emergent two-dimensional (2D) phase appears when the driving frequency exceeds a critical value, at which a dimension-raising phase transition takes place. We find that the nonequilibrium feature of the system could qualitatively change the finite temperature critical behavior of the emergent 2D phase and make it different from its equilibrium counterpart. A four-dimensional generalization and experimental realizations of the proposed model based on a programmable reconfiguration technique in optical tweezers setups have also been discussed.

William R. Schief

Taiki Haga

G. V. Klimachev

Yoshihiko Nonomura, Yusuke Tomita

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.

Dagne Wordofa Tola, Mulugeta Bekele

Abstract Phase transitions play a central role in statistical physics and are well understood in systems at thermal equilibrium. However, their nonequilibrium counterparts remain less explored because of the lack of a unified theoretical framework. In this study, we examine the potential of deep learning, specially convolutional neural networks (CNN), to detect nonequilibrium phase transitions (NEPT) in a 2D Ising model-like square lattice ferromagnetic system under effective parameter h . Without this parameter ( h = 0 ), we generate equilibrium spin configurations using the standard Metropolis algorithm as usual. With h ≠ 0 , we generate nonequilibrium spin configurations using an effective Glauber update rule which breaks detailed balance. While the former is used to train CNN, the later is not subsequently described by the usual Boltzmann-Gibbs distribution rather used to test the model. The study shows that the trained CNN can distinguish between ordered and disordered nonequilibrium steady states and accurately predict the critical temperature of the system undergoing NEPT. Finite size scaling analysis of the model’s output (perdition) reproduces critical exponents that agree with theoretical expectations, indicating that this method provides a strong, data driven approach for examining nonequilibrium critical phenomena.