Entropy of Folding of the Triangular Lattice

TL;DR

This paper calculates the folding entropy of a triangular lattice by relating it to a 3-coloring problem, providing an exact value using Baxter's formula, thus advancing understanding of lattice folding configurations.

Contribution

It establishes a novel equivalence between lattice folding enumeration and a 3-coloring problem, deriving an exact entropy value using Baxter's solution.

Findings

Folding entropy per triangle is approximately 1.2087.

Folding problem is equivalent to a 3-coloring problem of bonds.

Provides an exact formula for the folding entropy.

Abstract

The problem of counting the different ways of folding the planar triangular lattice is shown to be equivalent to that of counting the possible 3-colorings of its bonds, a dual version of the 3-coloring problem of the hexagonal lattice solved by Baxter. The folding entropy Log q per triangle is thus given by Baxter's formula q=sqrt(3)(Gamma[1/3])^(3/2)/2pi =1.2087...