Eur. Phys. J. B (2015) 88: 205
https://doi.org/10.1140/epjb/e2015-60362-4

Regular Article

Universality in four-dimensional random-field magnets

¹ Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK
² Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK

^a e-mail: nikolaos.fytas@coventry.ac.uk

Received: 5 May 2015
Received in final form: 26 June 2015
Published online: 10 August 2015

Abstract

We investigate the universality aspects of the four-dimensional random-field Ising model (RFIM) using numerical simulations at zero temperature. We consider two different, in terms of the field distribution, versions of the model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and system sizes. Using as finite-size measures the sample-to-sample fluctuations of the order parameter of the system, we propose, for both types of distributions, estimates of the critical field h_c and the critical exponent ν of the correlation length, the latter suggesting that the two models in four dimensions share the same universality class.