Hard Squares for z = -1

2007/09/27 by R. J. Baxter, Baxter, R. J.
Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.0709.4324

10 pages, 3 figures, 4 tables; two additional references

arxiv created 2007/11/21 · arxiv updated 2009/12/01

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 = 4 cos² (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.

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