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-$\frac{1}{2}$ $J_1-J_2-J_3$ 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. 
A. Bob\'ak, T. Lu\v{c}ivjansk\'y, M. \v{Z}ukovi\v{c}, M. Borovsk\'y   and T. Balcerzak
cond-mat.stat-mech