Weak-universal critical behavior and quantum critical point of the exactly soluble spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg and quartic Ising interactions

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.