  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 $J_1 < 0$ between nearest-neighbour pairs and $J_2 < 0$ between
next-nearest neighbour pairs of spins. We present results for the ground-state
energy as a function of the frustration parameter $R = J_2 /|J_1|$. 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.
