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

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.