On the Decay of Correlations in the Random Field Ising Model
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.
Communications in Mathematical Physics
- Pub Date:
- August 2018
- Mathematical Physics;
- Mathematics - Probability;
- 16 pages. Proof reorganized for better readability. To appear in Comm. Math. Phys