Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model

TL;DR

This paper investigates the non-Markovian persistence behavior in a one-dimensional non-equilibrium kinetic Ising model at the PC transition, revealing significant changes in dynamical exponents compared to equilibrium cases.

Contribution

It provides numerical analysis of persistence exponents and autocorrelation functions at the PC transition in a 1D non-equilibrium Ising model, highlighting non-Markovian effects.

Findings

Persistence exponent $ heta$ is affected by the PC transition.

Autocorrelation exponent $ u$ shows drastic change at the transition.

The process becomes non-Markovian near the PC critical point.

Abstract

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent $\Theta$ and the exponent $lambda$ characterising the two-time autocorrelation function of the total magnetization under non-equilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.