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Log-Sobolev inequality for the φ42 and φ43 measures

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Published version
Peer-reviewed

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Abstract

jats:titleAbstract</jats:title>jats:pThe continuum and measures are shown to satisfy a log‐Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that their susceptibility is bounded. In particular, this applies to all coupling constants in any finite volume, and uniformly in the volume in the entire high temperature phases of the and  models.</jats:p>jats:pThe proof uses a general criterion for the log‐Sobolev inequality in terms of the Polchinski (renormalisation group) equation, a recently proved remarkable correlation inequality for Ising models with general external fields, the Perron–Frobenius theorem, and bounds on the susceptibilities of the and measures obtained using skeleton inequalities.</jats:p>

Description

Keywords

4901 Applied Mathematics, 4902 Mathematical Physics, 4904 Pure Mathematics, 49 Mathematical Sciences, 10 Reduced Inequalities

Journal Title

Communications on Pure and Applied Mathematics

Conference Name

Journal ISSN

0010-3640
1097-0312

Volume Title

Publisher

Wiley
Sponsorship
European Commission Horizon 2020 (H2020) ERC (851682 SPINRG)