Random Matrix Theory and Classical Statistical Mechanics: Spin Models

Abstract

We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper. We show that the statistical properties of these spectra can serve as a criterion of integrability. It provides also an operational numerical method to locate integrable varieties. In particular, we distinguish the notions of integrability and criticality considering the two examples of the three-dimensional Ising critical point and the two-dimensional three-state Potts critical point. For complex spectra which appear frequently in the context of transfer matrices, we show that the notion of independence of eigenvalues for integrable models still holds.

19 pages, RevTex 9 PostScript figures

References in corpus (4)

• Quantum mechanics of lattice gas automata. I. One particle plane waves and potentials
• Energy level statistics of the two-dimensional Hubbard model at low filling
• The Spectrum of the two dimensional Hubbard model at low filling
• Spectral Properties of Statistical Mechanics Models

Cited by in corpus (6)

• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains
• Nearest-neigbor spacing distributions of the beta-Hermite ensemble of random matrices
• A random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids
• Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition
• Integrability of the critical point of the Kagomé three-state Potts mode