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1 A Spin- 3/2 Ising Model on a Square Lattice

N. Sh. Izmailian

Published Mar 13, 1996• 12 citations
OpenAlex

Abstract

The spin - 3/2 Ising model on a square lattice is investigated. It is shown that this model is reducible to an eight - vertex model on a surface in the parameter space spanned by coupling constants J, K, L and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space.

Related papers

A spin-3/2 Ising model on a square lattice

N. Sh. Izmailian

The spin-3/2 Ising model described by the most general Hamiltonian with up-down symmetry, −βH=Σ〈ij〉{JS i S j +KS 2 i S 2 j +LS 3 i S 3 j +M/2(S i S 3 j +S j S 3 i )}−ΔΣi S 2 i , is investigated on a square lattice. It is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants J, K, L, and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space. Consequently, the critical behavior and, in particular, the critical temperature for the second-order phase transitions of the model is found exactly.

arXiv:hep-th/9603080•Journal of Experimental and Theoretical Physics Letters•Feb 1, 1996•13 citations

Two-dimensional XXZ -Ising model on a square-hexagon lattice

J. S. Valverde, Onofre Rojas, S. M. de Souza

We study a two-dimensional XXZ -Ising model on a square-hexagon (denoted for simplicity by 4-6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the XXZ -Ising model on 4-6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.

arXiv:0809.2015•Physical Review E•Apr 1, 2009•14 citations

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David W. Wood

A vertex model problem on the honeycomb lattice is reduced to an eight-vertex model problem which satisfies the free-fermion condition. An Ising model in which only triplet coupling terms are present on a decorated version of the triangular lattice is equivalent to this free-fermion model, thus providing an example of a pure three-spin interaction which has the conventional Ising-like logarithmic singularity in the specific heat, independently of the values of the coupling constants.

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Local three-spin correlations in the free-fermion and planar Ising models

R. J. Baxter, T. C. Choy

Abstract A number of local three-spin correlations are calculated exactly for various related ferromagnetic two-dimensional solvable models in statistical mechanics.They are the square lattice free-fermion model, the equivalent checkerboard Ising model, and the anisotropic triangular, honeycomb and square lattice Ising models. The different results are all applications of a single unifying formula.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jun 8, 1989•21 citations

Diagrammatical Techniques for Two-Dimensional Ising Models. III. Ising Model to Vertex Model

Tohru Morita, Kazuyuki Tanaka

It is shown that an application of the techniques of division and integration of lattice sites reduces Ising models to equivalent vertex models. When the Ising model is on a two-dimensional lattice and no crossing occurs for any two of line segments connecting two lattice sites between which an interaction exists, the equivalent vertex model is shown to be a free-fermion vertex model. An argument is also given to show that the present method provides a method of expressing the partition function of a general Ising model on the square lattice, with noncrossing interactions within a square plaquette, in terms of a determinant of a 4×4 matrix.

Journal of the Physical Society of Japan•Mar 15, 1993•3 citations

Mixed-spin Ising model on the union jack lattice

Adam Lipowski, Tomoya Horiguchi

We show that the mixed-spin Ising model on the union jack lattice with S= 1/2 and S=1 spin operators placed on different sublattices is equivalent to the eight-vertex model. On a two-dimensional manifold in a parameter space, the model corresponds to the symmetric eight-vertex model and thus is solvable. We locate exactly a coexistence surface between two ordered phases of the mixed-spin model. This surface is bounded by a bicritical line with continuously changing exponents.

Journal of Physics A Mathematical and General•May 7, 1995•27 citations
The spin-3/2 Ising model described by the most general Hamiltonian with up-down symmetry, −βH=Σ〈ij〉{JS i S j +KS 2 i S 2 j +LS 3 i S 3 j +M/2(S i S 3 j +S j S 3 i )}−ΔΣi S 2 i , is investigated on a square lattice. It is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants J, K, L, and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space. Consequently, the critical behavior and, in particular, the critical temperature for the second-order phase transitions of the model is found exactly.
We study a two-dimensional XXZ -Ising model on a square-hexagon (denoted for simplicity by 4-6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the XXZ -Ising model on 4-6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.
It is shown that an application of the techniques of division and integration of lattice sites reduces Ising models to equivalent vertex models. When the Ising model is on a two-dimensional lattice and no crossing occurs for any two of line segments connecting two lattice sites between which an interaction exists, the equivalent vertex model is shown to be a free-fermion vertex model. An argument is also given to show that the present method provides a method of expressing the partition function of a general Ising model on the square lattice, with noncrossing interactions within a square plaquette, in terms of a determinant of a 4×4 matrix.