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arXiv · 1611.02193

Liouville field theory and log-correlated Random Energy Models

Xiangyu Cao·Pierre Le Doussal·Alberto Rosso·Raoul Santachiara
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Abstract

An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.

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Xiangyu Cao, Pierre Le Doussal, Alberto Rosso, Raoul Santachiara. 2017-06-15. Liouville field theory and log-correlated Random Energy Models. https://doi.org/10.1103/physrevlett.118.090601

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