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Improved Peierls Argument for High-Dimensional Ising Models

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Abstract

We consider the low-temperature expansion for the Ising model on \(\mathbb{Z}^d ,d \geqslant 2\), 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.

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Lebowitz, J.L., Mazel, A.E. Improved Peierls Argument for High-Dimensional Ising Models. Journal of Statistical Physics 90, 1051–1059 (1998). https://doi.org/10.1023/A:1023205826704

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  • DOI: https://doi.org/10.1023/A:1023205826704

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