The 3-d Random Field Ising Model at zero temperature

Abstract

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.

8 pages, 3 PostScript Figures

References in corpus (2)

• Glassy transition in the three-dimensional random field Ising model
• Ordering temperatures and critical exponents in Ising spin glasses

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