Glassy phase and freezing of log-correlated Gaussian potentials

Abstract

In this paper, we consider the Gibbs measure associated to a logarithmically correlated random potential (including two dimensional free fields) at low temperature. We prove that the energy landscape freezes and enters in the so-called glassy phase. The limiting Gibbs weights are integrated atomic random measures with random intensity expressed in terms of the critical Gaussian multiplicative chaos. This could be seen as a first rigorous step in the renormalization theory of super-critical Gaussian multiplicative chaos.

37 pages

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Cited by in corpus (4)

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• Multiplicative chaos measures for a random model of the Riemann zeta function
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• The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase