  Spin-1/2 Ising-Heisenberg model with XYZ Heisenberg pair interaction and two
different Ising quartic interactions is exactly solved with the help of the
generalized star-square transformation, which establishes a precise mapping
equivalence with the corresponding eight-vertex model on a square lattice
generally satisfying Baxter's zero-field (symmetric) condition. The
investigated model exhibits a remarkable weak-universal critical behavior with
two marked wings of critical lines along which critical exponents vary
continuously with the interaction parameters. Both wings of critical lines
merge together at a very special quantum critical point of the infinite order,
which can be characterized through diverging critical exponents. The
possibility of observing reentrant phase transitions in a close vicinity of the
quantum critical point is related to a relative strength of the exchange
anisotropy in the XYZ Heisenberg pair interaction.
