Depinning of a domain wall in the 2d random-field Ising model

TL;DR

This study investigates the depinning transition of a domain wall in a 2D random-field Ising model, revealing percolative movement and critical exponents near the threshold, supported by numerical simulations and scaling theory.

Contribution

It provides a detailed analysis of the depinning transition, including critical exponents and crossover behavior, combining numerical data with analytical scaling arguments.

Findings

Domain wall moves percolatively even with weak disorder

Depinning critical exponent matches percolation theory (beta=5/36)

Critical region shrinks with decreasing disorder

Abstract

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent beta=5/36 as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent beta'=0 at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments.