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Communications in Theoretical Physics

Dynamical Phase Transitions in the Disordered Two-Dimensional XY Model

Ce-Jun Liu, Jia-Zhen Hu

Published Mar 15, 1996• 0 citations
Publisher

Abstract

We study the time evolution of the distance between two configurations of the site-disordered two-dimensional model submitted to metropolis dynamics on a square lattice. For concentrations between and , dynamical transitions and three temperature regimes, similar to the case of pure model, are found.
DOI
10.1088/0253-6102/25/2/179

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The 2D XY model is studied by Monte Carlo simulations where two configurations subjected to the same thermal noise are compared. The authors observe three temperature regimes: a high-temperature phase where the two configurations meet, an intermediate phase where they do not meet but their distance becomes independent of the initial distance and a low-temperature phase where the distance remembers for very long the initial distance. The two transition temperatures T 1 =1.61+or-0.01 and T 2 =0.95+or-0.05 are estimated by means of finite-size scaling.
We study the time evolution of the distance between two configurations submitted to the same thermal noise for the 3 d ± J Ising spin glass. We observe three temperature regimes: a high-temperature regime where the distances vanishes in the long-time limit. An intermediate-temperature regime where the distance has a nonzero limit independent of the initial distance. A low-temperature regime where the distance in the long time limit seems to depend upon the initial distance. For the sake of comparison, we have repeated our simulations for the ferromagnetic case.
The site-diluted Ising ferromagnet is investigated on a square lattice, within short-time-dynamics numerical simulations, for different site concentrations. The dynamical exponents θ and z are obtained and it is shown that these exponents do depend strongly on the disorder, exhibiting a clear breakdown of universality, characterized by relative variations of nearly 100% in the range of site concentrations investigated. In what concerns the static exponents β and ν, universality is preserved within the error bars.
The computer simulation method was used to study phase transitions in a two-dimensional site-diluted 3-state Potts model. Systems with linear dimensions Lx L=N, L=10/160 at a spin concentration p=1.00, 0.80 are considered. The numerical data obtained indicate that in a pure 3-state Potts model on a square lattice, a phase transition of the second order is observed in accordance with the theory. The introduction of disorder in the form of non-magnetic impurities (p=0.80) in the 3-state Potts model preserves the phase transition of the second order. Keywords: Potts model, Monte Carlo method, thermodynamic parameters, disorder.