Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder

TL;DR

This study uses Monte Carlo simulations to analyze the depinning transition in a 2D random-field Ising model, revealing a new universality class with critical exponents influenced by disorder type and strength.

Contribution

It identifies a new dynamic universality class for the depinning transition in the 2D RFIM and explores how disorder form and strength affect critical exponents.

Findings

Critical exponents vary with disorder form and strength.

Depinning transition belongs to a new universality class.

Crossover from second- to first-order transition observed for uniform disorder.

Abstract

With Monte Carlo methods, we investigate the universality class of the depinning transition in the two-dimensional Ising model with quenched random fields. Based on the short-time dynamic approach, we accurately determine the depinning transition field and both static and dynamic critical exponents. The critical exponents vary significantly with the form and strength of the random fields, but exhibit independence on the updating schemes of the Monte Carlo algorithm. From the roughness exponents $\zeta, \zeta_{loc}$ and $\zeta_s$, one may judge that the depinning transition of the random-field Ising model belongs to the new dynamic universality class with $\zeta \neq \zeta_{loc}\neq \zeta_s$ and $\zeta_{loc} \neq 1$. The crossover from the second-order phase transition to the first-order one is observed for the uniform distribution of the random fields, but it is not present for the Gaussian distribution.