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Hard squares with negative activity

Paul Fendley·Kareljan Schoutens·Hendrik van Eerten
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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.

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Paul Fendley, Kareljan Schoutens, Hendrik van Eerten. 2004-08-24. Hard squares with negative activity. https://doi.org/10.1088/0305-4470%2F38%2F2%2F002

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