Year: 2026
Type: preprint
Abstract: For the sinh-Gordon model (without external mass term), we show that the log-Sobolev inequality holds uniformly in the lattice and volume regularisations for all parameters in the regime in which the Gaussian multiplicative chaos has second moments. This implies that infinite-volume ``massless'' sinh-Gordon measures on $\mathbb{R}^2$ satisfying all Osterwalder--Schrader axioms exist and that they have exponential decay of correlations (are ``massive''). The proof uses the Polchinski equation method for log-Sobolev inequalities. The required estimates on the renormalised potential are established using simple perturbation theoretic bounds, valid for absolutely monotone potentials, and an extension of the correlation inequality of Ding--Song--Sun to potentials in the GHS class. This inequality is proved also by using a variant of the Polchinski equation through the maximum principle.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214242016