Hard squares with negative activity
Statistical Mechanics
2009-11-10 v1 Mathematical Physics
Combinatorics
math.MP
Abstract
We show that the hard-square lattice gas with activity z= -1 has a number of remarkable properties. We conjecture that all the eigenvalues of the transfer matrix are roots of unity. They fall into groups (``strings'') evenly spaced around the unit circle, which have interesting number-theoretic properties. For example, the partition function on an M by N lattice with periodic boundary condition is identically 1 when M and N are coprime. We provide evidence for these conjectures from analytical and numerical arguments.
Cite
@article{arxiv.cond-mat/0408497,
title = {Hard squares with negative activity},
author = {Paul Fendley and Kareljan Schoutens and Hendrik van Eerten},
journal= {arXiv preprint arXiv:cond-mat/0408497},
year = {2009}
}
Comments
8 pages