Liouville field theory and log-correlated Random Energy Models
Statistical Mechanics
2017-06-16 v2 Disordered Systems and Neural Networks
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
An exact mapping is established between the 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.
Keywords
Cite
@article{arxiv.1611.02193,
title = {Liouville field theory and log-correlated Random Energy Models},
author = {Xiangyu Cao and Pierre Le Doussal and Alberto Rosso and Raoul Santachiara},
journal= {arXiv preprint arXiv:1611.02193},
year = {2017}
}
Comments
5 pages, 3 figures + 10 pages, 2 figures; accepted version