Log-Sobolev inequality for the φ 2 4 $\varphi ^4_2$ and φ 3 4 $\varphi ^4_3$ measures

IF 3.1 1区 数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2023-10-16 DOI:10.1002/cpa.22173
Roland Bauerschmidt, Benoit Dagallier
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引用次数: 0

Abstract

The continuum φ 2 4 $\varphi ^4_2$ and φ 3 4 $\varphi ^4_3$ 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 φ 2 4 $\varphi ^4_2$ and φ 3 4 $\varphi ^4_3$  models.

The 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 φ 2 4 $\varphi ^4_2$ and φ 3 4 $\varphi ^4_3$ measures obtained using skeleton inequalities.

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φ24$\varphi^4_2$和φ34$\varphi^4_3$测度的Log-Sobolev不等式
在磁化率有界的最优假设下,连续统φ24$\varphi^4_2$和φ34$\varphi^4_3$测度在格正则化中一致满足log-Sobolev不等式。特别地,这适用于任何有限体积中的所有耦合常数,并且在φ24$\varphi^4_2$和φ34$\varphi^4_3$模型的整个高温阶段的体积中均匀地适用。
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来源期刊
CiteScore
6.70
自引率
3.30%
发文量
59
审稿时长
>12 weeks
期刊介绍: Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.
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