A Note on Exponential Decay in the Random Field Ising Model

Federico Camia, Jianping Jiang*, Charles M. Newman

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension.

Original languageEnglish
Pages (from-to)268-284
Number of pages17
JournalJournal of Statistical Physics
Volume173
Issue number2
Early online date30 Aug 2018
DOIs
Publication statusPublished - Oct 2018

Keywords

  • Coupling
  • Exponential decay
  • Kertész line
  • Random cluster model
  • Random field Ising model

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