Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

TL;DR

This paper studies the depinning phase transition of domain walls in 2D magnets using Hamiltonian equations, revealing a new universality class distinct from effective equations.

Contribution

It introduces a Hamiltonian-based approach to analyze depinning transitions, highlighting a different universality class from traditional effective models.

Findings

Determined the transition field numerically.

Measured static and dynamic critical exponents.

Identified a new universality class for the Hamiltonian dynamics.

Abstract

Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.