Liouville field theory and log-correlated Random Energy Models

Xiangyu Cao 1 Alberto Rosso 1 Raoul Santachiara 1 Pierre Le Doussal 2 Pierre Le Doussal 2

Physical Review Letters, American Physical Society, 2017, 118 (9), pp.090601

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.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. LPTENS - Laboratoire de Physique Théorique de l'ENS