  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.
