Nonequilibrium dynamics of fully frustrated Ising models at T=0

TL;DR

This study investigates the nonequilibrium dynamics of two fully frustrated Ising models at zero temperature, revealing a universal scaling law for relaxation times and field-dependent autocorrelation behavior through Monte Carlo simulations.

Contribution

It introduces a detailed analysis of relaxation dynamics and autocorrelation scaling in frustrated Ising models after a quench to zero temperature, highlighting universal and field-dependent features.

Findings

Relaxation time scales as L^2 log(L) for both models.

Autocorrelation functions exhibit logarithmic corrections at critical points.

Autocorrelation exponent varies with applied magnetic field.

Abstract

We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength, $h=H T k_B$, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T=0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, $L$, we define and measure sample dependent "first passage time", $t_r$, which is the number of Monte Carlo steps until the energy is relaxed to the ground-state value. The distribution of $t_r$, in particular its mean value, $< t_r(L) >$, is shown to obey the scaling relation, $< t_r(L) > \sim L^2 \ln(L/L_0)$, for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H=0 and at the field-induced Kosterlitz-Thouless transition, however the autocorrelation exponent is found to be $H$ dependent.