Spectral Properties of Statistical Mechanics Models

Details Spectral Properties of Statistical Mechanics Models Spectral Properties of Statistical Mechanics Models

1996-04-08

arxiv.org/abs/cond-mat/9604042v1

Physics

Condensed Matter

4 pages, 1 Revtex file and 4 postscript figures tarred, gzipped and uuencoded

Scientific paper

10.1088/0305-4470/29/18/006

The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we have found eigenvalue repulsion as for the Gaussian orthogonal ensemble in random matrix theory. By contrast, in integrable regimes we have found eigenvalue independence leading to a Poissonian behavior, and, for some points, level clustering. These first examples from classical statistical mechanics suggest that the conjecture of integrability successfully applied to quantum spin systems also holds for classical systems.

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