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

Nicolas Sourlas
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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 $δh$). 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/ ν$ . We find different values of $ ν$ for the different random field distributions, in disagreement with universality.

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Nicolas Sourlas. 1998-10-19. Universality in Random Systems: the case of the 3-d Random Field Ising model. https://doi.org/10.1016/s0010-4655(99)00308-2

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