An $n$ -component continuous-spin model with a tricritical point is solved exactly in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$. Its properties are derived and are compared with the results of experiments and approximate calculations. The model leads to an analytical description of the features of tricritical points and suggests the use of an approximation procedure for discrete spin systems which is a substantial qualitative and quantitative improvement on mean-field theory.An $n$-component continuous-spin model with a tricritical point is solved exactly in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$. Its properties are derived and are compared with the results of experiments and approximate calculations. The model leads to an analytical description of the features of tricritical points and suggests the use of an approximation procedure for discrete spin systems which is a substantial qualitative and quantitative improvement on mean-field theory.

Physical review. B, Solid stateMay 1, 197543 citations

Tricritical Properties of Antiferromagnetic Ising Model on the Square Lattice

A. Bobák, M. Borovský, T. Lučivjanský +1 more

The Ising square lattice model with nearest-neighbor (nn) interactions ( $J_1$ ) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions ( $J_2$ ) or a magnetic field (or both) leads to the non solvability of the model and only some approximate solutions are possible. In this brief report we will review some results obtained within effective field theory. We will show that besides second-order transitions there are also lines of first-order transitions and the coordinates of tricritical points are calculated.The Ising square lattice model with nearest-neighbor (nn) interactions ($J_1$) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions ($J_2$) or a magnetic field (or both) leads to the non solvability of the model and only some approximate solutions are possible. In this brief report we will review some results obtained within effective field theory. We will show that besides second-order transitions there are also lines of first-order transitions and the coordinates of tricritical points are calculated.

arXiv:1512.05929Dec 18, 20150 citations

n

-component continuous-spin model with a tricritical point is solved exactly in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$. Its properties are derived and are compared with the results of experiments and approximate calculations. The model leads to an analytical description of the features of tricritical points and suggests the use of an approximation procedure for discrete spin systems which is a substantial qualitative and quantitative improvement on mean-field theory.

The Ising square lattice model with nearest-neighbor (nn) interactions (

J_1

) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions (

J_2

) or a magnetic field (or both) leads to the non solvability of the model and only some approximate solutions are possible. In this brief report we will review some results obtained within effective field theory. We will show that besides second-order transitions there are also lines of first-order transitions and the coordinates of tricritical points are calculated.