Folding the Square-Diagonal Lattice

Details Folding the Square-Diagonal Lattice Folding the Square-Diagonal Lattice

1998-03-04

arxiv.org/abs/cond-mat/9803051v1

Physics

Condensed Matter

Statistical Mechanics

uses harvmac, epsf, 48 pages, 27 figures

Scientific paper

10.1016/S0550-3213(98)00320-4

We study the problem of "phantom" folding of the two-dimensional square lattice, in which the edges and diagonals of each face can be folded. The non-vanishing thermodynamic folding entropy per face $s \simeq .2299(1)$ is estimated both analytically and numerically, by successively mapping the model onto a dense loop model, a spin model and a new 28 Vertex, 4-color model. Higher dimensional generalizations are investigated, as well as other foldable lattices.

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