Phase transitions in the Ising antiferromagnet on the frustrated honeycomb lattice

We present a study of the thermal phase transitions between paramagnetic (PM) and antiferromagnetic (AF) phases in the $J_1$-$J_2$ frustrated honeycomb Ising model. In this model, the competition between AF first-neighbour ($J_1>0$) and second-neighbour ($J_2>0$) interactions can lead to different levels of frustration by tuning the ratio $J_2/J_1$. By adopting a cluster mean-field approach, we provide a description of the nature of phase transitions and the role of frustration on the thermodynamics of the model for $0⩽J_2/J_1<1/4$. Our results indicate that the Néel temperature vanishes at $J_2/J_1=1/4$ and only second-order phase transitions are present in the PM-AF phase boundary. Moreover, the thermodynamic quantities are affected by the strongly competitive scenario that takes place for $J_2/J_1\approx 1/4$. In particular, we found a round maximum in the specific heat and a finite entropy plateau within the PM phase, suggesting strong frustration effects. Therefore, our results suggest that a regime of strong frustration can be found near the PM-AF phase transition for $J_2/J_1\approx 1/4$.