Improved Peierls Argument for High Dimensional Ising Models

Abstract

We consider the low temperature expansion for the Ising model on ${\mathbb{Z}}^d$, $d\ge 2$, with ferromagnetic nearest neighbor interactions in terms of Peierls contours. We prove that the expansion converges for all temperatures smaller than $Cd(\log d{)}^{-1}$, which is the correct order in $d$.

12 pages, in TeX, e-mail addresses: [email protected], [email protected]

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