Universality in four-dimensional random-field magnets

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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.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Nikolaos G. Fytas
    • 1
  • Panagiotis E. Theodorakis
    • 2
  1. 1.Applied Mathematics Research CentreCoventry UniversityCoventryUK
  2. 2.Department of Chemical EngineeringImperial College LondonLondonUK

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