Pre-freezing transition in Boltzmann-Gibbs measures associated with log-correlated fields

TL;DR

This paper investigates phase transitions in Boltzmann-Gibbs measures linked to log-correlated Gaussian fields, extending the understanding of pre-freezing and freezing phenomena across dimensions using Gaussian multiplicative chaos theory.

Contribution

It generalizes the pre-freezing and freezing phenomena of annealed exponents to arbitrary dimensions, supported by rigorous Gaussian multiplicative chaos results.

Findings

Verification of pre-freezing and freezing phenomena in multiple dimensions

Extension of Fyodorov's predictions using rigorous mathematical frameworks

Identification of phase transition behaviors in multifractal properties

Abstract

We consider Boltzmann-Gibbs measures associated with log-correlated Gaussian fields as potentials and study their multifractal properties which exhibit phase transitions. In particular, the pre-freezing and freezing phenomena of the annealed exponent, predicted by Fyodorov using a modified replica-symmetry-breaking ansatz, are generalised to arbitrary dimension and verified using results from Gaussian multiplicative chaos theory.