  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.
