标题： 临界环模型是精确可解的 显示英文标题

标题： Critical loop models are exactly solvable

摘要： 在二维临界环模型中，包括$O(n)$和 Potts 模型，谱是已知的，以及一些结构常数或它们的比值。 使用数值共形Bootstrap方法，我们研究了最简单的4点结构常数$235$。 对于每个结构常数，我们找到一个解析表达式，作为两个因子的乘积：1）一个与共形维度相关的通用函数，由Barnes的双重Gamma函数构建，2）一个与环权重相关的多项式函数，其次数满足一个简单的上界。 我们猜想所有结构常数都是这种形式。 对于几个4点函数，我们在格点环模型中构建了相应的可观测量。 从数值格点结果中，我们提取了既不依赖于格点大小也不依赖于格点耦合的振幅比值。 这些比值与相应的4点结构常数的比值一致。 显示英文摘要

摘要： In two-dimensional critical loop models, including the $O(n)$ and Potts models, the spectrum is exactly known, as are a few structure constants or ratios thereof. Using numerical conformal bootstrap methods, we study $235$ of the simplest 4-point structure constants. For each structure constant, we find an analytic expression as a product of two factors: 1) a universal function of conformal dimensions, built from Barnes' double Gamma function, and 2) a polynomial function of loop weights, whose degree obeys a simple upper bound. We conjecture that all structure constants are of this form. For a few 4-point functions, we build corresponding observables in a lattice loop model. From numerical lattice results, we extract amplitude ratios that depend neither on the lattice size nor on the lattice coupling. These ratios agree with the corresponding ratios of 4-point structure constants.