A note on exponential decay in the random field Ising model

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 (1) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (2) 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.

arXiv comment16 pages, minor revision

References in corpus (4)

• The Random-Cluster Model
• On the decay of correlations in the random field Ising model
• On the Kertész line: Thermodynamic versus Geometric Criticality
• On the Kertész line: Some rigorous bounds

Cited by in corpus (7)

• Exponential decay of correlations in the 2D random field Ising model
• A power-law upper bound on the correlations in the 2D random field Ising model
• Exponential decay of correlations in the two-dimensional random field Ising model at zero temperature
• Correlation length of the two-dimensional random field Ising model via greedy lattice animal
• Exponential decay of correlations in the two-dimensional random field Ising model
• Absence of Replica Symmetry Breaking in Finite Fifth Moment Random Field Ising Model
• Approximation algorithms for the random-field Ising model