 96343 C.E. Pfister, Y. Velenik
 Large Deviations and Continuum Limit in the 2D Ising model
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Jul 23, 96

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Abstract. We study the 2D Ising model in a rectangular box
$\Lambda_L$ of linear size $O(L)$. We determine the exact asymptotic behaviour
of the large deviations of the magnetization $\sum_{t\in\Lambda_L}\sigma(t)$
when $L\ra\infty$ for values of the parameters of the model corresponding to
the phase coexistence region, where the order parameter $m^*$ is strictly
positive. We study in particular boundary effects due to an arbitrary
realvalued boundary magnetic field. Using the selfduality of the model
a large part of the analysis consists in deriving properties
of the covariance function $\bra\,\sigma(0)\sigma(t)\,\ket$, as
$\t\\ra\infty$, at dual values of the parameters of the model.
To do this analysis we establish new results about the hightemperature
representation of the model. These results are valid for dimensions $D\geq 2$
and up to the critical temperature. We then study the Gibbs measure
conditionned by $\{\,\,\sum_{t\in \Lambda_L}\sigma(t)m\Lambda_L\,\leq
\Lambda_LL^{c}\,\}$, with $0<c<1/4$ and $m^*<m<m^*$. We construct the
continuum limit of the model and describe the limit by the solutions of a
variational problem of isoperimetric type.
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