Spectral gap in mean-field $\mathcal{O}(n)$-model

Abstract

We study the dependence of the spectral gap for the generator of the Ginzburg-Landau dynamics for all \emph{$\mathcal{O}(n)$-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.

arXiv comment44 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

References in corpus (15)

• Heat conduction in the disordered harmonic chain revisited
• Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems
• Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
• The mixing time evolution of Glauber dynamics for the mean-field Ising model
• Introduction to a renormalisation group method
• A very simple proof of the LSI for high temperature spin systems
• Simplicity of eigenvalues in the Anderson model
• Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift
• Sharp interpolation inequalities on the sphere : new methods and consequences
• Log-Sobolev inequality for the continuum sine-Gordon model
• Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential
• Rigorous scaling law for the heat current in disordered harmonic chain
• Censored Glauber Dynamics for the mean field Ising Model
• Hydrodynamic limit for a disordered harmonic chain
• A note on Harris' ergodic theorem, controllability and perturbations of harmonic networks

Cited by in corpus (2)

• Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions
• Spectral Analysis of Discrete Metastable Diffusions