Canonical Finite-Volume Algorithms

Abstract

As we have seen in Sect. 3.8, the response functions and the various thermodynamic coefficients are expressed as correlation functions of the type:

$$\begin{aligned} {\mathcal T}\big ( \partial ^{\alpha _1} G_1(h) \, \partial ^{\alpha _2} G_2(h) \ldots \big ) \; , \quad h \in {\mathcal A}_d \; , \end{aligned}$$

(5.1)

and variations of it, such as the Kubo formula treated in Sect. 7.1. In this Chapter, we use the previously introduced auxiliary algebras and propose a canonical finite-volume algorithm for computing the above correlation functions. Our main goals for the Chapter are to integrate the algorithm in a broader context and then to summarize for the reader the concrete steps of the algorithm, as applied to disordered homogeneous solids. The error estimates are the subjects of the following Chapters.