Work

Phase transition for weakly interacting focusing Gibbs measures with harmonic potential

Year: 2026

Type: preprint

Abstract: In this paper, we study the Gibbs measures on Euclidean spaces associated to the focusing nonlinear Schrödinger equation with harmonic potential and critical non linearity whose coupling constant tends to 0, a question initially posed by Brydges-Slade (1996) for the $Φ^4_2$-model on $\mathbb{T}^2$. In dimension one and in the higher dimensional cases (with radial assumption), we establish a critical threshold below which the frequency-truncated measures converge to the base Gaussian measure (possibly with a renormalized $L^2$ cut-off) while, in the supercritical regime, we prove non-convergence of the frequency-truncated measures, even up to a subsequence.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.11608

Authors: Greco, Damiano, Wang, Yuzhao

Institutions: Maxwell Institute for Mathematical Sciences, Dalian University of Technology, Dalian University, University of Birmingham

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Dynamics of singular stochastic nonlinear dispersive PDEs, Probabilistic study of nonlinear Schrödinger equations on compact domains, G6276981034

OpenAlex ID: W7168301804

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