Theoretical Study of the Frustrated Ising Antiferromagnet on the Honeycomb Lattice

TL;DR

This paper investigates how next-next-nearest-neighbor interactions influence the phase transitions and critical behavior of a frustrated spin-1/2 Ising antiferromagnet on a honeycomb lattice, revealing a tricritical point.

Contribution

It provides a theoretical analysis of the phase diagram of the frustrated honeycomb Ising model including the effects of $J_3$ interactions, identifying a tricritical point and transition nature change.

Findings

Identification of a tricritical point in the phase diagram.

Change from second-order to first-order phase transition.

Influence of $J_3$ interactions on critical properties.

Abstract

We study effects of the next-next-nearest-neighbour antiferromagnetic ($J_3 < 0$) interaction on critical properties (or phase diagram) of the frustrated spin-$\frac{1}{2}$ $J_1-J_2-J_3$ Ising antiferromagnet on the honeycomb lattice by using the effective-field theory with correlations. Beside the ground-state energy, we find that there is a region of $J_3 < 0$ in which the frustrated honeycomb lattice antiferromagnet exhibits a tricritical point, at which the phase transition changes from the second order to the first one on the line between N\'eel antiferromagnetic and paramagnetic phases.