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