On the Decay of Correlations in the Random Field Ising Model
Abstract
In a celebrated 1990 paper, Aizenman and Wehr proved that the twodimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodictheoretic in nature and does not provide any quantitative information. This article proves the first quantitative version of the AizenmanWehr 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 August 2018
 DOI:
 10.1007/s0022001830850
 arXiv:
 arXiv:1709.04151
 Bibcode:
 2018CMaPh.362..253C
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 82B44;
 60K35
 EPrint:
 16 pages. Proof reorganized for better readability. To appear in Comm. Math. Phys