The log-Sobolev inequality for spin systems of higher order interactions


Konstantopoulos, Takis and Papageorgiou, Ioannis (2019) The log-Sobolev inequality for spin systems of higher order interactions. ArXiV.

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Abstract

We study the infinite-dimensional log-Sobolev inequality for spin systems on $\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that the one site measure without a boundary $e^{-\phi(x)}dx/Z$ satisfies a log-Sobolev inequality and we determine conditions so that the infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete application, we prove that a certain class of nontrivial Gibbs measures with non-quadratic interaction potentials on an infinite product of Heisenberg groups satisfy the log-Sobolev inequality.

Item Type: Article
Uncontrolled Keywords: math.PR, math.PR, math-ph, math.FA, math.MP, 60K35, 26D10, 39B62, 22E30
Depositing User: Symplectic Admin
Date Deposited: 27 Sep 2019 10:36
Last Modified: 06 Sep 2023 00:35
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3048489
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