The 3-d Random Field Ising Model at zero temperature

Details The 3-d Random Field Ising Model at zero temperature The 3-d Random Field Ising Model at zero temperature

1997-04-10

arxiv.org/abs/cond-mat/9704088v1

Physics

Condensed Matter

8 pages, 3 PostScript Figures

Scientific paper

10.1209/epl/i1997-00379-x

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $L$ in three dimensions. For each random field configuration we vary the ferromagnetic coupling strength $J$. We find that in the infinite volume limit the magnetization is discontinuous in $J$. The energy and its first $J$ derivative are continuous. The approch to the thermodynamic limit is slow, behaving like $L^{-p}$ with $p \sim .8$ for the gaussian distribution of the random field. We also study the bimodal distribution $h_{i} = \pm h$, and we find similar results for the magnetization but with a different value of the exponent $p \sim .6 $. This raises the question of the validity of universality for the random field problem.

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