发表机构
University of Chicago; Harvard University（芝加哥大学; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种自举方法，利用正性、运动方程和随机耦合期望值，通过线性规划与半定规划推导淬火无序经典系统的无序平均界限，并在二维稀释伊辛模型和一维无序接触过程中验证，后者界限的扭结区域与Griffiths区相关。
AI 中文摘要
我们引入了一种自举方法，用于推导具有淬火无序的经典统计系统中无序平均可观测量的界限。自举的三个主要成分是概率测度系综的正性、无序平均的运动方程以及随机耦合变量的显式期望值。这些成分共同导致了一个在无序平均空间上的线性规划问题。通过进一步利用两副本Gram矩阵的正性，我们还提出了一个半定规划问题，该问题产生了两副本关联函数的界限。我们使用两个例子演示了该方法：二维随机位点稀释伊辛模型和一维无序接触过程。对于后一个例子，自举界限表现出一个多扭结区域，我们将其与Griffiths区域相关联，其有限尺寸缩放分析得出的典型相关长度指数与已知值在数值上吻合良好。
英文摘要
We introduce a bootstrap method for deriving bounds on disorder-averaged observables in classical statistical systems with quenched disorder. The three main ingredients of the bootstrap are the positivity of ensembles of probability measures, disorder-averaged equations of motion, and explicit expectation values of random coupling variables. Together, these ingredients lead to a linear programming problem over the space of disorder averages. By further employing the positivity of the two-replica Gram matrix, we also formulate a semidefinite programming problem that produces bounds on two-replica correlators. We demonstrate the method using two examples: the two-dimensional random site-diluted Ising model and the one-dimensional disordered contact process. For the latter example, the bootstrap bounds exhibit a region of multiple kinks that we relate to the Griffiths region, whose finite-size scaling analysis yields a typical correlation length exponent in good numerical agreement with the known value.
Comments15 pages, 9 figures
