Coarsening Dynamics of Nonequilibrium Chiral Ising Models

TL;DR

This paper studies the nonequilibrium coarsening behavior of a one-dimensional chiral Ising model, revealing continuously varying critical exponents and identifying a new universality class through simulations and spectral analysis.

Contribution

It introduces a novel class of coarsening dynamics in chiral Ising models with continuously varying exponents, expanding understanding of nonequilibrium phase transitions.

Findings

Power-law decay of kink density with variable exponents

Continuous variation of scaling exponents with model parameters

Identification of a new universality class for chiral coarsening

Abstract

We investigate a nonequilibrium coarsening dynamics of a one-dimensional Ising spin system with chirality. Only spins at domain boundaries are updated so that the model undergoes a coarsening to either of equivalent absorbing states with all spins + or -. Chirality is imposed by assigning different transition rates to events at down (+-) kinks and up (-+) kinks. The coarsening is characterized by power-law scalings of the kink density $\rho \sim t^{-\delta}$ and the characteristic length scale $\xi \sim t^{1/z}$ with time $t$. Surprisingly the scaling exponents vary continuously with model parameters, which is not the case for systems without chirality. These results are obtained from extensive Monte Carlo simulations and spectral analyses of the time evolution operator. Our study uncovers the novel universality class of the coarsening dynamics with chirality.