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Journal of Applied Physics

MCRG study of d-dimensional random field Ising models

Elisabeth Busk Rasmussen, M. A. Novotny, David Paul Landau

Published Mar 1, 1982• 31 citations
Publisher

Abstract

A Monte Carlo Renormalization Group method has been used to study d-dimensional hypercubic Ising models in random fields (±H). For d = 4 our results are consistent with classical critical behavior. For d = 3 we find a sharp transition with critical exponents which are apparently modified by the random field. We find no sharp transition for d = 2.

DOI
10.1063/1.330669

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中国科学通报：英文版•Jan 1, 1990•0 citations
A Monte Carlo Renormalization Group method has been used to study d-dimensional hypercubic Ising models in random fields (±H). For d = 4 our results are consistent with classical critical behavior. For d = 3 we find a sharp transition with critical exponents which are apparently modified by the random field. We find no sharp transition for d = 2.
The nature of the three-dimensional random-field Ising model with a bimodal probability distribution is investigated using finite-time scaling combined with the Monte Carlo renormalization group method, in the presence of a linearly varying temperature. Our results support the existence of a first-order phase transition for this model, obtained through reducing the influence of finite-size effects. The critical exponents are estimated to be ν = 0.74(3), β = 0.27(1), α = − 0.023(5), and γ = 1.48(3) with corrections to the scaling. The Rushbrooke scaling law is satisfied with these exponents, and in turn identifies the asymptotic critical behavior.
The phase transition of the three-dimensional random field Ising model with a discrete (+or-h) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the magnetization appears to be discontinuous, the specific heat appears to saturate, indicating no latent heat. Sample-to-sample fluctuations of the susceptibility are consistent with the droplet picture for the transition.