Solvable Decorated Ising Model with Superexchange Interaction

Exact Results of the Mixed-Spin Ising Model on a Decorated Square Lattice With Two Different Decorating Spins of Integer Magnitudes

“…77 and references cited therein). Among the systems, which belong to the class of exactly solved decorated Ising models, one could mention, at least, the original ferrimagnetic model introduced by Syozi [99][100][101][102][103][104] as well as the models with higher decorating spins. 49,50 It is worth mentioning that exact solutions of these spin model systems have furnished answers to interesting questions from the academic point of view (scaling and universality hypothesis, re-entrant phase transitions) as well as from the experimental viewpoint (dilution, technological application of ferrimagnets).…”

The effect of uniaxial crystal-field anisotropy on magnetic properties of the superexchange antiferromagnetic Ising model

“…Of course, in some regions the stability of disordered phases extends down to zero temperature in agreement with the ground-state phase diagram. One should also note that our model exhibits essentially the same critical behavior as Fisher and Mishiyama and Nara models [1,2,4]. This is obvious, since the decoration of the lattice by finite number of atoms cannot lead to a change of the universality class of the model.…”

“…However, this model is only one of a number of similar exactly solvable antiferromagnetic lattices and its simple generalization leads to a series of other models which could display a variety of interesting features. To the best of our knowledge, only two generalizations of Fisher model have been investigated so far, namely, the superexchange Ising model on the kagome lattice [3] and the decorated Ising model which is the combination of the Fisher model and the Shiozi-Miyazima model of dilute-Ising spin system [4]. Considering this fact, the main purpose of the present work is to generalize the original superexchange model for arbitrary values of decorating atoms including the effect of the uniaxial crystal-field anisotropy as well.…”

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

“…On the other hand, a rigorous investigation of the magneticfield effect on magnetic properties of the 2D Ising models still remains an open topic due to the lack of closed-form exact solution for the partition function at finite magnetic fields. At present, there are known just a few mixed-spin Ising models which allow an exact study of the magnetic-field effect in 2D, namely, the spin-1/2 Ising model on a kagomé lattice [5][6][7], the spin-1/2 Fisher super-exchange model on a square lattice [8,9] and its another extensions [10][11][12][13]. All these models involve the action of the longitudinal magnetic field on two-thirds of all the lattice sites.…”

“…Taking into account the aforementioned facts, we propose in this paper a novel mixed-spin Ising model on a decorated triangular lattice in a longitudinal magnetic field for which the closed-form exact solution can be derived. The proposed model is somewhat reminiscent of the generalized Fisher super-exchange model on a square lattice [8][9][10][11][12][13], but its main novelty lies in definition on a non-bipartite triangular lattice, which provides a possible playground for a new type of spin frustration. Besides the ground-state analysis, our attention is focused on the study of the zero-temperature magnetization process, critical behaviour and magnetocaloric properties of the system.…”