Poisson approximations for the Ising model

Details Poisson approximations for the Ising model Poisson approximations for the Ising model

2006-05-15

arxiv.org/abs/math/0605395v2

Mathematics

Probability

25 pages, 1 figure

Scientific paper

10.1007/s10955-006-9033-y

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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