Spectral gap in mean-field $\mathcal O(n)$-model
Mathematical Physics
2020-12-02 v2 Analysis of PDEs
math.MP
Probability
Spectral Theory
Abstract
We study the dependence of the spectral gap for the generator of the Ginzburg-Landau dynamics for all \emph{-models} with mean-field interaction and magnetic field, below and at the critical temperature on the number of particles. For our analysis of the Gibbs measure, we use a one-step renormalization approach and semiclassical methods to study the eigenvalue-spacing of an auxiliary Schr\"odinger operator.
Keywords
Cite
@article{arxiv.1909.12241,
title = {Spectral gap in mean-field $\mathcal O(n)$-model},
author = {Simon Becker and Angeliki Menegaki},
journal= {arXiv preprint arXiv:1909.12241},
year = {2020}
}
Comments
44 pages, 10 figures. This preprint includes the previous results for the mean-field $\mathcal O(n)$-model and contains new results (sharp spectral gap for the critical temperature-case) with improved presentation. The second part of the previous version, on the chain of oscillators, will be outsourced into an independent preprint