Tricritical Properties of Antiferromagnetic Ising Model on the Square Lattice

TL;DR

This paper investigates the phase transition behavior of the antiferromagnetic Ising model on a square lattice with next-nearest-neighbor interactions, identifying tricritical points and transition lines using effective field theory.

Contribution

It provides the first calculation of tricritical points in the antiferromagnetic Ising model with extended interactions on the square lattice.

Findings

Existence of lines of first-order and second-order phase transitions.

Coordinates of tricritical points are explicitly calculated.

Effective field theory successfully describes complex transition behavior.

Abstract

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.