$d=0$中的无序场论和分布Zeta函数
Disordered Field Theory in $d=0$ and Distributional Zeta-Function
摘要：
最近，我们介绍了一种新的技术，用于计算具有猝灭随机性的系统的平均自由能。这种技术的基本工具是分布zeta函数。分布ζ函数是一个复函数，其在原点的导数产生系统的平均自由能作为两个贡献之和：第一个是一个级数，其中模型的配分函数的所有整数矩都有贡献;第二个不能写为整数矩的级数，可以尽可能小。本文给出了一个严格的数学证明，证明了零维空间中的无序$λφ^{4}$模型的平均自由能可以用分布zeta函数方法求得.我们得到了该模型的平均自由能的解析表达式。
英文摘要：
Recently we introduced a new technique for computing the average free energy of a system with quenched randomness. The basic tool of this technique is a distributional zeta-function. The distributional zeta-function is a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which can not be written as a series of the integer moments, can be made as small as desired. In this paper we present a mathematical rigorous proof that the average free energy of one disordered $λφ^{4}$ model defined in a zero-dimensional space can be obtained using the distributional zeta-function technique. We obtain an analytic expression for the average free energy of the model.
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