On the decay of correlations in the random field Ising model

Abstract

In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodic-theoretic in nature and does not provide any quantitative information. This article proves the first quantitative version of the Aizenman-Wehr theorem. The proof introduces a new method for proving decay of correlations that may be interesting in its own right. A fairly detailed sketch of the main ideas behind the proof is also included.

16 pages. Proof reorganized for better readability. To appear in Comm. Math. Phys

References in corpus (1)

• Absence of replica symmetry breaking in the random field Ising model

Cited by in corpus (4)

• Exponential decay of correlations in the 2D random field Ising model
• A note on exponential decay in the random field Ising model
• A power-law upper bound on the correlations in the 2D random field Ising model
• On minimizing curves in a Brownian potential