无序O（n）圈模型与耦合共形场论
Disordered O(n) Loop Model and Coupled Conformal Field Theories
摘要：
本文分析了二维随机背景中波动环的一类模型。该模型被配制为O（n）自旋模型与淬火非均匀相互作用。使用副本方法，模型被映射到$M$层O（n）模型的$M\to 0$极限，该模型通过$ϕ_{1,3}$主字段相互耦合。重整化群流计算在解耦临界点附近，通过围绕伊辛点（$n=1$）的一个展开，改变$n$作为一个连续的参数。单圈β函数表明在自回避行走点（$n=0$）附近存在强耦合相（$0<n<n_*$），在伊辛点附近存在红外固定点（$n_*<n<1$）。对于固定点，计算有效中心电荷。能量算符和自旋算符的标度维数得到了两圈阶。简要讨论了与无规键$q$态Potts模型的关系。
英文摘要：
A family of models for fluctuating loops in a two dimensional random background is analyzed. The models are formulated as O(n) spin models with quenched inhomogeneous interactions. Using the replica method, the models are mapped to the $M\to 0$ limits of $M$-layered O(n) models coupled each other via $ϕ_{1,3}$ primary fields. The renormalization group flow is calculated in the vicinity of the decoupled critical point, by an epsilon expansion around the Ising point ($n=1$), varying $n$ as a continuous parameter. The one-loop beta function suggests the existence of a strongly coupled phase ($0<n<n_*$) near the self-avoiding walk point ($n=0$) and a line of infrared fixed points ($n_*<n<1$) near the Ising point. For the fixed points, the effective central charges are calculated. The scaling dimensions of the energy operator and the spin operator are obtained up to two-loop order. The relation to the random-bond $q$-state Potts model is briefly discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
