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

Abstract

Spin-1/2 Ising-Heisenberg model with XY Z 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 XY Z Heisenberg pair interaction. FIGURE 1. The elementary unit cell of the spin-1/2 Ising-Heisenberg model. Full (empty) circles denote positions of the Heisenberg (Ising) spins, thick solid line represents the pairwise XY Z Heisenberg interaction between the apical Heisenberg spins and both types of broken lines connect spins involved in the quartic Ising interactions. Thin solid lines connecting four Ising spins are guide for eyes only.This paper is so organized. In the following section, we will describe the hybrid Ising-Heisenberg model and recall basic steps of the exact mapping procedure to the zero-field eight-vertex model. The most interesting results for the ground-state and finite-temperature phase diagrams, which are supported by a detailed analysis of critical exponents, are subsequently presented in the next section. Finally, some concluding remarks are mentioned along with a brief summary of the most important scientific achievements in the last section. 0 1 2 3 4 0.00 0.05 0.10 0.15 J 2 / J z = 1.0 0.5 0.5 0.25 0.25 J y / J x = 0.5 J 1 / J z = 1.0 J x / J z I II k B T c / J z FIGURE 3. The dimensionless critical temperature as a function of the anisotropy parameter J x /J z for the Ising-Heisenberg model with the XY Z exchange anisotropy (J x = J y ) when a strength of the one quartic Ising-type interaction is fixed (J 1 /J z = 1.0) and that of another one quartic Ising-type interaction J 2 /J z varies.