Lattice Green functions: the \(d\)-dimensional face-centered cubic lattice, \(d = 8, 9, 10, 11, 12\). (English) Zbl 1357.35096
A lattice Green function (LGF) of the \(d\)-dimensional face-centered cubic lattice is given by a \(d\)-fold integral whose expansion around the origin is hard to obtain as the dimension goes higher. There is a recursive method to generate the expansion of LGF. In the paper, the authors show the strength and the limit of the method by producing some series and corresponding linear differential equations for \(d=8,9,\dots,12\).
Reviewer: Utkir A. Rozikov (Tashkent)
MSC:
35J08 | Green’s functions for elliptic equations |
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
34B27 | Green’s functions for ordinary differential equations |
34A30 | Linear ordinary differential equations and systems |