Theoretical Study of the Frustrated Ising Antiferromagnet on the Honeycomb Lattice

We study effects of the next-next-nearest-neighbour antiferromagnetic (J(3) < 0) interaction on critical properties (or phase diagram) of the frustrated spin-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 Neel antiferromagnetic and paramagnetic phases.