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Pre-freezing transition in Boltzmann-Gibbs measures associated with log-correlated fields (1711.11555v1)
Published 30 Nov 2017 in math.PR, cond-mat.dis-nn, and cond-mat.stat-mech
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.
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