Spectral Gap in Mean-Field $${\mathcal {O}}(n)$$-Model

Abstract

AbstractWe study the dependence of the spectral gap for the generator of the Ginzburg–Landau dynamics for all $$\mathcal O(n)$$ O ( n ) -models with mean-field interaction and magnetic field, below and at the critical temperature on the number N 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 Schrödinger operator.