Liouville field theory and log-correlated Random Energy Models
arXiv:1611.02193 · doi:10.1103/PhysRevLett.118.090601
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.
5 pages, 3 figures + 10 pages, 2 figures; accepted version