Criticality of the random field Ising model in and out of equilibrium: a nonperturbative functional renormalization group description

TL;DR

This paper demonstrates that the critical behavior of the random-field Ising model differs between equilibrium and out-of-equilibrium states below a critical dimension, using a non-perturbative functional renormalization group approach.

Contribution

It introduces a non-perturbative functional renormalization group method to analyze the criticality of the random-field Ising model out of equilibrium, revealing a new universality class below a critical dimension.

Findings

Out-of-equilibrium and equilibrium critical points are in different universality classes below d≈5.1.

Above this dimension, avalanches become irrelevant and the critical points coincide.

Provides a framework for computer simulations to verify the theoretical predictions.

Abstract

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasi-statically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension $d_{DR}\approx 5.1$. We demonstrate this by implementing a non-perturbative functional renormalization group for the associated dynamical field theory. Above $d_{DR}$, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.