Tricritical behaviour of the frustrated Ising antiferromagnet on the honeycomb lattice

•We investigate a tricritical behaviour of the frustrated Ising model on a honeycomb lattice.•We present results for the ground-state energy as a function of the frustration parameter.•We present phase diagram of the model by using an effective-field theory with correlations.•We also discuss effect of the cluster-size on the existence and location of a tricritical point in the phase diagram.

We use the effective-field theory with correlations based on different cluster sizes to investigate phase diagrams of the frustrated Ising antiferromagnet on the honeycomb lattice with isotropic interactions of the strength J1<0J1<0 between nearest-neighbour pairs and J2<0J2<0 between next-nearest neighbour pairs of spins. We present results for the ground-state energy as a function of the frustration parameter R=J2/|J1|R=J2/|J1|. We find that the cluster-size has a considerable effect on the existence and location of a tricritical point in the phase diagram at which the phase transition changes from the second order to the first one.