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Poisson approximations for the Ising model

David Coupier
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Abstract

A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field $a=a(n)$ tends to $-\infty$ and the pair potential $b$ remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case.

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David Coupier. 2006-05-17. Poisson approximations for the Ising model. https://doi.org/10.1007/s10955-006-9033-y

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