Cao Xiangyu, Rosso Alberto, Santachiara Raoul, Le Doussal Pierre
LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
CNRS-Laboratoire de Physique Théorique de l'École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France.
Phys Rev Lett. 2017 Mar 3;118(9):090601. doi: 10.1103/PhysRevLett.118.090601. Epub 2017 Feb 28.
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.
在c≥25的刘维尔场论（LFT）与二维高斯自由场加对数禁闭势中热粒子的吉布斯测度统计之间建立了精确映射。通过结合共形引导和一步复制对称破缺方法，精确地得到了能量景观最小值位置的概率分布。LFT中的算符乘积展开使我们能够揭示对数相关随机能量类的新的普适行为。给出了高精度数值测试。
