Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-08-24
J. Phys. A38 (2005) 315
Physics
Condensed Matter
Statistical Mechanics
8 pages
Scientific paper
10.1088/0305-4470/38/2/002
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.
Eerten Hendrik van
Fendley Paul
Schoutens Kareljan
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