A Lattice Spanning-Tree Entropy Function

TL;DR

This paper evaluates a lattice spanning-tree entropy function explicitly using standard functions and applies it to derive limiting values of the triangular lattice Green function.

Contribution

It provides a direct evaluation of the spanning-tree entropy function in terms of standard functions, enabling new insights into lattice Green functions.

Findings

Explicit evaluation of the entropy function in standard functions

Derivation of limiting values for the triangular lattice Green function

Enhanced understanding of lattice entropy and Green functions

Abstract

The function $$W(aq,b)=\int\int_0^{2\pi}\ln[1-a\cos x-b\cos y-(1-a-b)\cos(x+y)]dxdy$$ which expresses the spanning-tree entropy for various two dimensional lattices, for example, is evaluated directly in terms of standard functions. It is applied to derive several limiting values of the triangular lattice Green function.