# Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium

## TL;DR

This paper benchmarks a nonperturbative functional renormalization group method on the random elastic manifold model, successfully reproducing known critical properties and supporting its application to disordered systems in and out of equilibrium.

## Contribution

It demonstrates the effectiveness of the nonperturbative functional renormalization group approach on the random elastic manifold model, confirming known critical exponents and scaling functions.

## Key findings

- Recovered known critical exponents and scaling functions
- Validated the approach for equilibrium and depinning cases
- Supported previous results on universality classes and critical dimensions

## Abstract

Criticality in the class of disordered systems comprising the random-field Ising model (RFIM) and elastic manifolds in a random environment is controlled by zero-temperature fixed points that must be treated through a functional renormalization group. We apply the nonperturbative functional renormalization group approach that we have previously used to describe the RFIM in and out of equilibrium [Balog-Tarjus-Tissier, Phys. Rev. B 97, 094204 (2018)] to the simpler and by now well-studied case of the random elastic manifold model. We recover the main known properties, critical exponents and scaling functions, of both the pinned phase of the manifold at equilibrium and the depinning threshold in the athermally and quasi-statically driven case for any dimension $0<d\leq 4$. This successful benchmarking of our theoretical approach gives strong support to the results that we have previously obtained for the RFIM, in particular concerning the distinct universality classes of the equilibrium and out-of-equilibrium (hysteresis) critical points below a critical dimension $d_{DR}\approx 5.1$.