Papers › Liouville field theory and log-correlated Random Energy Models
Liouville field theory and log-correlated Random Energy Models
Xiangyu Cao, Pierre Le Doussal, Alberto Rosso, Raoul Santachiara
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An exact mapping is established between the c≥25 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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