Pre-freezing transition in Boltzmann-Gibbs measures associated with log-correlated fields
Probability
2017-12-01 v1 Disordered Systems and Neural Networks
Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.1711.11555,
title = {Pre-freezing transition in Boltzmann-Gibbs measures associated with log-correlated fields},
author = {Mo Dick Wong},
journal= {arXiv preprint arXiv:1711.11555},
year = {2017}
}