Universality in Random Systems: the case of the 3-d Random Field Ising model

Abstract

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $6\le L\le 90$ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each random field configuration we vary the ferromagnetic coupling strength J and compute the ground state exactly. We examine the case of different random field probability distributions: gaussian distribution, zero width bimodal distribution h_{i} = \pm 1, wide bimodal distribution h_{i} = \pm 1 +δh (with a gaussian $\delta h$). We also study the case of the randomly diluted antiferromagnet in a field,which is thought to be in the same universality class. We find that in the infinite volume limit the magnetization is discontinuous in J and we compute the relevant exponent, which, according to finite size scaling, equals $1/\nu$ . We find different values of $\nu$ for the different random field distributions, in disagreement with universality.

7 pages, 3 figures

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