Random-field Ising model: Insight from zero-temperature simulations

P.E. Theodorakis, N.G. Fytas

    Research output: Contribution to journalArticle

    7 Citations (Scopus)


    We enlighten some critical aspects of the three-dimensional (d = 3) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model. By implementing a computational approach thatmaps the ground-state of the systemto themaximum-flowoptimization 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 systems sizesV = L ×L ×L, where L denotes linear lattice size and Lmax = 156. Using as finite-size measures the sample to- sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field hc and the critical exponent v of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian random-field Ising model at the best-known value of the critical field provide the magnetic exponent ratio β/v with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.
    Original languageEnglish
    Article number43003
    JournalCondensed Matter Physics
    Issue number4
    Publication statusPublished - 2014

    Bibliographical note

    This article is published in an open access journal and is available to download at: http://www.icmp.lviv.ua/journal/zbirnyk.80/43003/art43003.pdf


    • Finite-size scaling
    • Graph theory
    • Random-field Ising model


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