Condensed Matter Physics, 2014, vol. 17, No. 4, 43003
DOI:10.5488/CMP.17.43003
arXiv:1501.02338
Title:
Randomfield Ising model: Insight from zerotemperature simulations
Author(s):

P.E. Theodorakis
(Department of Chemical Engineering, Imperial College London, SW7 2AZ, London, United Kingdom)
,


N.G. Fytas
(Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, United Kingdom)

We enlighten some critical aspects of the threedimensional (d=3) randomfield Ising model (RFIM) from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian RFIM and an equalweight trimodal RFIM. By implementing a computational approach that maps the groundstate of the system to the maximumflow optimization problem of a network, we employ the most uptodate version of the pushrelabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of randomfield values and systems sizes V=LxLxL, where L denotes linear lattice size and L_{max}=156. Using as finitesize measures the sampletosample fluctuations of various quantities of physical and technical origin, and the primitive operations of the pushrelabel algorithm, we propose, for both types of distributions, estimates of the critical field h_{max} and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian RFIM at the bestknown value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinitelimit size extrapolation of energy and orderparameterbased noise to signal ratios related to the selfaveraging properties of the model, as well as the critical slowing down aspects of the algorithm.
Key words:
randomfield Ising model, finitesize scaling, graph theory
PACS:
05.50.+q, 75.10.Hk, 64.60.Cn, 75.10.Nr
