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

TL;DR

This paper introduces efficient numerical methods, including finite-size scaling and reweighting extrapolation, to analyze the critical behavior of the three-dimensional random-field Ising model, emphasizing response functions and correction-to-scaling techniques.

Contribution

It provides a detailed combined numerical scheme for the RFIM, including a zero-temperature approach, fluctuation-dissipation formula, and an extension of the quotients method for critical exponent estimation.

Findings

Confirmed the single universality class of the 3D RFIM

Developed a generalized fluctuation-dissipation formula for correlation functions

Extended the quotients method to estimate the specific heat exponent

Abstract

It was recently shown [Phys. Rev. Lett. {\bf 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 $\alpha$ 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.