Hard Squares for z = -1

Date

2011

Authors

Baxter, Rodney

Journal Title

Journal ISSN

Volume Title

Publisher

Birkhauser Verlag

Abstract

The hard square model in statistical mechanics has been investigated for the case when the activity z is -1. For cyclic boundary conditions, the characteristic polynomial of the transfer matrix has an intriguingly simple structure, all the eigenvalues x being zero, roots of unity, or solutions of x3 = 4cos2(πm/N). Here we tabulate the results for lattices of up to 12 columns with cyclic or free boundary conditions and the two obvious orientations. We remark that they are all unexpectedly simple and that for the rotated lattice with free or fixed boundary conditions there are obvious likely generalizations to any lattice size.

Description

Keywords

Keywords: lattice models; statistical mechanics; transfer matrices

Citation

Source

Annals of Combinatorics

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

Restricted until

2037-12-31