The 3d random field Ising model at zero temperature

1997/04/10 by J C Anglès d'Auriac, J. -C. Anglès d'Auriac, Nicolas Sourlas +1 · 5 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1209/epl/i1997-00379-x

8 pages, 3 PostScript Figures

arxiv created 1997/04/10 · openalex publication_date 1997/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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 approach to the thermodynamic limit is slow, behaving like L − p with p ∼ 0.8 for the Gaussian distribution of the random field. We also study the bimodal distribution h i = ± h , and we find similar results for the magnetization but with a different value of the exponent p ∼ 0.6. This raises the question of the validity of universality for the random field problem.

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