  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.
