Year: 2007
Type: preprint
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 x^3 = 4 cos^2 (pi*m/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.
Source: arXiv (Cornell University)
Author: Baxter, R. J.
Institution: Australian National University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951595443