The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

TL;DR

This paper studies the depinning transition of driven interfaces in the random-field Ising model across different dimensions, identifying the upper critical dimension as five and linking the behavior to the quenched Edward-Wilkinson universality class.

Contribution

It determines the upper critical dimension for the depinning transition in the random-field Ising model and clarifies its universality class.

Findings

Upper critical dimension is five.

Order parameter follows a scaling law at low temperatures.

System belongs to the quenched Edward-Wilkinson universality class.

Abstract

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.