The correlated cluster mean-field approach to the frustrated Ising model on the honeycomb lattice

We study the $J_1$-$J_2$ Ising model on the honeycomb lattice, considering ferromagnetic interactions between first neighbors ($J_1$) and antiferromagnetic interactions between second neighbors ($J_2$). Our analysis is based on the correlated cluster mean field theory, which is adapted to incorporate competing interactions, providing estimates for the behavior of magnetization, internal energy, entropy, specific heat, and short-range correlations of the model. Our results indicate that the transition temperature of the ferromagnetic-paramagnetic phase transition decreases toward zero as the frustration maximum ($J_2/J_1 = -1/4$) is approached, and the thermodynamic quantities indicate only continuous phase transitions for $-1/4<J_2/J_1 \leq 0$. The critical temperature and the nature of phase transitions provided by the correlated cluster mean-field method are in excellent agreement with very recent Monte Carlo simulations for the model. Furthermore, the specific heat exhibits a broad maximum within the PM phase under strong frustration, suggesting the onset of a correlated paramagnetic state with high entropy content at low temperatures. Therefore, our findings support that frustration not only suppresses the ferromagnetic long-range order, but also drives significant changes in the thermodynamics and short-range correlations of the model.