RANDOM-MATRIX THEORY AND CLASSICAL STATISTICAL-MECHANICS - VERTEX MODELS

A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymme tric eight-vertex model is studied using random matrix theory (eigenva lue spacing distribution and spectral rigidity). For Yang-Baxter integ rable cases, including free-fermion solutions, we found a Poissonian b ehavior, whereas level repulsion close to the Wigner distribution is f ound for nonintegrable models. For the asymmetric eight-vertex model, however, the level repulsion can also disappear, and the Poisson distr ibution be recovered on (non Yang-Baxter integrable) algebraic varieti es, the so-called disorder varieties. We also present an infinite set of algebraic varieties which are stable under the action of an infinit e discrete symmetry group of the parameter space. These varieties are possible loci for free parafermions. Using our numerical criterion, we tested the generic calculability of the model on these algebraic vari eties.