Paul Fendley et al 2005 J. Phys. A: Math. Gen. 38 315 doi:10.1088/0305-4470/38/2/002
Paul Fendley1, Kareljan Schoutens2 and Hendrik van Eerten2
Show affiliationsWe 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 × 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.
15A18 Eigenvalues, singular values, and eigenvectors
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 2 (14 January 2005)
Received 28 September 2004
Published 15 December 2004
Paul Fendley et al 2005 J. Phys. A: Math. Gen. 38 315
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