Numerical study of metastable states in the T=0 RFIM

TL;DR

This paper numerically investigates the complexity and distribution of metastable states in the T=0 RFIM on various lattices, revealing how their organization relates to out-of-equilibrium phase transitions in magnetization.

Contribution

It provides the first detailed numerical analysis of metastable state complexities in the T=0 RFIM across different lattice types and connects these to phase transition phenomena.

Findings

Metastable state complexity varies with external field and disorder.

Distribution of metastable states influences out-of-equilibrium phase transitions.

Change in metastable state distribution correlates with hysteresis loop behavior.

Abstract

We study numerically the number of single-spin-flip stable states in the T=0 Random Field Ising Model (RFIM) on random regular graphs of connectivity $z=2$ and $z=4$ and on the cubic lattice. The annealed and quenched complexities (i.e. the entropy densities) of the metastable states with given magnetization are calculated as a function of the external magnetic field. The results show that the appearance of a (disorder-induced) out-of-equilibrium phase transition in the magnetization hysteresis loop at low disorder can be ascribed to a change in the distribution of the metastable states in the field-magnetization plane.