Replica trick to calculate means of absolute values: applications to stochastic equations
Replica trick to calculate means of absolute values: applications to stochastic equations
复制标题
计算绝对值均值的复制技巧：在随机方程中的应用
DOI：
10.1088/0305-4470/24/21/011
复制
发表时间：
1991
期刊：
影响因子：
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通讯作者：
J. Kurchan
中科院分区：
文献类型：
--
作者：
J. Kurchan
复制技巧的一个版本可以用来计算不是正定的函数的绝对值的平均值(以及经过一些修改的绝对值的平均对数)。这一技巧可以应用于随机方程的上下文中，其中必须计算每个解中随机函数的雅可比的绝对值。本文讨论了SK自旋玻璃“朴素”平均场方程平均解的计算，并将其推广到其它平均场方程(如TAP)。BRST超对称性被发现提供了一个有用的工具来揭示这些计算中的一些令人困惑的方面。提出的技巧为这些问题提供了一种可能的解决方案。
A version of the replica trick can be used to evaluate means of the absolute values of functions that are not positive-definite (and with some modifications the mean logarithm of the absolute value). This trick can be applied in the context of stochastic equations, where the absolute value of the Jacobian of the stochastic function in each solution must be computed. The calculation of the average number of solutions of the 'naive' mean field equations for the SK spin-glass is discussed, an extension of the considerations to other mean field equations (such as TAP) is straightforward. The BRST supersymmetry is found to provide a useful tool in uncovering some puzzling aspects in these calculations. The trick presented provides a possible solution to these problems.