%0 Journal Article
%T Hard squares with negative activity
%A Paul Fendley
%A Kareljan Schoutens
%A Hendrik van Eerten
%J Mathematics
%D 2004
%I arXiv
%R 10.1088/0305-4470/38/2/002
%X 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.
%U http://arxiv.org/abs/cond-mat/0408497v1