  The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction
and quartic Ising interactions is exactly solved by establishing a precise
mapping relationship with the corresponding zero-field (symmetric) eight-vertex
model. It is shown that the Ising-Heisenberg model with the ferromagnetic
Heisenberg interaction exhibits a striking critical behavior, which manifests
itself through re-entrant phase transitions as well as continuously varying
critical exponents. The changes of critical exponents are in accordance with
the weak universality hypothesis in spite of a peculiar singular behavior to
emerge at a quantum critical point of the infinite order, which occurs at the
isotropic limit of the Heisenberg interaction. On the other hand, the
Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction
surprisingly exhibits less significant changes of both critical temperatures as
well as critical exponents upon varying a strength of the exchange anisotropy
in the Heisenberg interaction.
