Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

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It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
©2016 American Physical Society. We are grateful to D. Yllanes and, especially, to L.A. Fernández for substantial help during several parts of this work. We also thank M. Picco and N. Sourlas for reading the manuscript. We were partly supported by MINECO, Spain, through research Contract No. FIS2012-35719-C02-01. Significant allocations of computing time were obtained in the clusters Terminus and Memento (BIFI). N.G.F. acknowledges financial support from a Royal Society Research Grant under No. RG140201 and from a Research Collaboration Fellowship Scheme of Coventry University.
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