English

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 c25c\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.

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