# Abstract

Large Deviations and Continuum Limit in the 2D Ising Model
C.-E. Pfister and Y. Velenik
Probab. Theory Relat. Fields
109,
435-506
(1997).
We study the 2D Ising model in a rectangular box of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization for values of the parameters of the model corresponding to the phase coexistence region, where the order parameter is strictly positive. We study in particular boundary effects due to an arbitrary real-valued boundary magnetic field. Using the self-duality of the model a large part of the analysis consists in deriving properties of the covariance function at dual values of the parameters of the model. To do this analysis we establish new results about the high-temperature representation of the model. These results are valid for dimensions greater or equal 2 and up to the critical temperature. We construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperimetric type, similar but not identical to the Wulff construction.

**Key words:**Ising model, large deviations, Wulff shape, variational problem, continuum limit, wetting phenomenon**Files:**PDF, Published version, bibtex