A universal form of slow dynamics in zero-temperature random-field Ising model

TL;DR

This paper derives an exact evolution equation for the zero-temperature random-field Ising model on a random graph, revealing a new class of slow dynamics and critical behavior through bifurcation analysis.

Contribution

It introduces an exact evolution equation for the model and uncovers a universal slow dynamics class with specific critical exponents.

Findings

Identification of a new class of cooperative slow dynamics

Exact bifurcation analysis revealing critical exponents

Universal behavior in zero-temperature RFIM dynamics

Abstract

The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial condition, we derive exactly an evolution equation for an order parameter. Through a bifurcation analysis of the obtained equation, we reveal a new class of cooperative slow dynamics with the determination of critical exponents.