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

Takis Konstantopoulos; Ioannis Papageorgiou

doi:10.1063/5.0176456

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arXiv · 1906.11980

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

Takis Konstantopoulos·Ioannis Papageorgiou

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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.

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BibTeX RIS

Takis Konstantopoulos, Ioannis Papageorgiou. 2019-06-27. The log-Sobolev inequality for spin systems of higher order interactions. https://doi.org/10.1063/5.0176456

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