Liouville Field Theory and Log-Correlated Random Energy Models

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 exa...

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Bibliographic Details
Published in:Physical review letters 2017-03, Vol.118 (9), p.090601-090601, Article 090601
Main Authors: Cao, Xiangyu, Rosso, Alberto, Santachiara, Raoul, Le Doussal, Pierre
Format: Article
Language:English
Subjects:
Condensed Matter
Confining
Energy distribution
Field theory
Landscapes
Liouville equations
Mathematical models
Mathematical Physics
Operators
Physics
Statistical Mechanics
Statistics
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Summary: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 the LFT allow us to unveil novel universal behaviors of the log-correlated random energy class. High-precision numerical tests are given.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.118.090601