Sharp phase transition in the grand canonical $\Phi^3$ measure at critical chemical potential

TL;DR

This paper investigates the phase transition in a two-dimensional Euclidean quantum field theory model, identifying a critical chemical potential where a sharp transition occurs, supported by analysis of Gaussian fluctuations and correlation decay.

Contribution

It establishes the existence of a sharp phase transition at a critical chemical potential for the grand canonical  measure, extending understanding of critical phenomena in quantum field theory.

Findings

Identified a critical chemical potential for the phase transition.

Proved correlation decay of Gaussian fluctuations at criticality.

Demonstrated divergence of the maximum of an approximating Gaussian process.

Abstract

We study the phase transition and critical phenomenon for the grand canonical $\Phi^3$ measure in two-dimensional Euclidean quantum field theory. The study of this measure was initiated by Jaffe, Bourgain, and Carlen--Fr\"ohlich--Lebowitz, primarily in regimes far from criticality. We identify a critical chemical potential and show that the measure exhibits a sharp phase transition at this critical threshold. At the critical threshold, the analysis is based on establishing the correlation decay of the Gaussian fluctuations in the partition function, combined with a coarse-graining argument to show divergence of the maximum of an approximating Gaussian process.