  Two conditions are derived for Ising models to show non-universal critical
behaviour, namely conditions concerning 1) logarithmic singularity of the
specific heat and 2) degeneracy of the ground state. These conditions are
satisfied with the eight-vertex model, the Ashkin-Teller model, some Ising
models with short- or long-range interactions and even Ising systems without
the translational or the rotational invariance.
