The random field Ising model in one and two dimensions: A renormalization group approach

Suzana Moss De Oliveira, M.A. Continentino and P.M.C. Oliveira

Physica A: Statistical Mechanics and its Applications, 1990, vol. 162, issue 3, 458-476

Abstract: We study the one- and two-dimensional random field Ising models, using a real space renormalization group approach. We consider a bimodal distribution such that the random field assumes the values of +H or −H with probabilities p and1 − p, respectively (instead of the usual case p = 12). We obtain the phase diagrams and exponents associated with the uniform (p = 0, 1) and the random field (p = 12) problems. Our results are consistent with the absence of a spontaneous magnetization for H ≠ 0 and p ≠ 0, 1 in d = 1, 2 even at zero temperature. We finally discuss the nature of the singularities in the thermodynamics quantities occurring at T = 0 for discrete values of the random field intensity. We compare these results with those obtained previously for the dilute antiferromagnet in a uniform field using the same approach.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:162:y:1990:i:3:p:458-476

DOI: 10.1016/0378-4371(90)90428-U

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