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

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

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.

Suggested Citation

  • De Oliveira, Suzana Moss & Continentino, M.A. & Oliveira, P.M.C., 1990. "The random field Ising model in one and two dimensions: A renormalization group approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 162(3), pages 458-476.
    • Handle: RePEc:eee:phsmap:v:162:y:1990:i:3:p:458-476
    DOI: 10.1016/0378-4371(90)90428-U
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    Cited by:

    1. Branco, N.S. & Chame, Anna, 1996. "Extraordinary transition for the anisotropic Heisenberg ferromagnet on a semi-infinite lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 487-498.

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