A tool for identifying the criticality in the disordered systems with metastable dynamics

Abstract

We tackle the question of criticality in disordered systems that exhibit metastable dynamics throughout the process of relaxation. We propose a tool for discovering the existence of nontrivial critical behaviour and showcase it on the nonequilibrium athermal random field Ising model, being a pivotal example of the nonequilibrium models of disordered systems. By this tool, we analysed the dependence of critical field on the disorder of the system using different initial setups, the traditional with all spins pointing downwards and those modified which consider the lattice having an interface of aforehand preset upward spins at some cross-section and the others having islands of preset upward spins with diameters smaller than the lattice size. Our results obtained in this way on the cubic three-dimensional, square two-dimensional and hexagonal two-dimensional lattices are in agreement with those found by traditional methods which evidences the applicability of the proposed tool.