Non-universal critical behaviour of a mixed-spin Ising model on the extended Kagomé lattice

Abstract

The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagomé lattice is solved by establishing a mapping correspondence with the eight-vertex model. When the parameter of uniaxial single-ion anisotropy tends to infinity, the model system becomes exactly solvable as the staggered eight-vertex model satisfying the free-fermion condition. The critical points within this manifold can be characterized by critical exponents from the standard Ising universality class. The critical points within another subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, can be approximated by corresponding results of the uniform eight-vertex model satisfying the zero-field condition. This coexistence surface is bounded by a line of bicritical points that have non-universal continuously varying critical indices.

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

“…Li et al [11] studied the mixed spin-1/2 and spin-3/2 quantum Heisenberg system on a square lattice with the double-time-temperature Green function method to investigate the effects of the nearest-and next-nearest-neighbor interactions between spins on the magnetic behavior of the system, especially on the compensation point. The system has also been investigated on the Bethe lattice [12] and two-fold Cayley tree [13] using the exact recursion relations, on the honeycomb lattice within the framework of an exact star-triangle mapping transformations [14], and on the extended Kagomé lattice [15] and union Jack (centered square) lattice [16] by establishing a mapping correspondence with the eightvertex model. Despite of all these equilibrium studies, as far as we know, the nonequilibrium aspects of this system have not been investigated.…”

Dynamic phase diagrams of a mixed spin-1 and spin-5/2 Ising system in an oscillating magnetic field

“…The dynamics of the mixed spin-1/2 and spin-1 Ising system has also investigated by using Glauber-type stochastic dynamics [11], the dynamical pair approximation [12], dynamic MC simulations and finite-sized scaling arguments [13], the MC simulations and the dynamical pair approximation [14], and the path probability method with point distribution [15]. The exact solution of the spin (1/2, 3/2) Ising system has also been studied on the Bethe lattice and a two-fold Cayley tree [16] by using the exact recursion relations, on the honeycomb lattice within the framework of an exact star-triangle mapping transformations [17], and on the extended Kagomé lattice [18] and union Jack (centered square) lattice [19] by establishing a mapping correspondence with the eight-vertex model. The exact formulation of the mixed spin (1, 3/2) Ising ferrimagnetic system on the Bethe lattice has been examined by using the exact recursion relations [20].…”

The effective-field study of a mixed spin-1 and spin-5/2 Ising ferrimagnetic system

“…Dynamics of the mixed spin-1/2 and spin-1 Ising system [23,24] has also been investigated by using the Glauber-type stochastic dynamics [25], the dynamical pair approximation [26], the dynamic MC simulations and finite-size scaling arguments [27], the MC simulations and the dynamical pair approximation [28,29] and the pair approximation with point distribution [30]. The exact solution of spins (1/2, 3/2) Ising system has also been studied on the Bethe lattice [31] and a two-fold Cayley tree [32] by using the exact recursion relations, on the honeycomb lattice within the framework of exact star-triangle mapping transformations [33], on the extended Kagomé lattice [34] and Union Jack (centered square) lattice [35] by establishing a mapping correspondence with the eight-vertex model. On the other hand, the exact formulation of the mixed spin (1, 3/2) Ising ferrimagnetic system on the Bethe lattice has been examined by using the exact recursion relations [36].…”