The phase transitions of the frustrated J₁-J₂ Ising model on the honeycomb lattice

We study the phase transitions of the frustrated J₁-J₂ Ising model on the honeycomb lattice using the non-perturbative first principle Monte Carlo simulations. Here J₁ 0 are the nearest and next-to-nearest couplings, respectively. In particular, the values of J₂/|J₁| = 0. 20, 0. 22, 0. 23, 0. 24, 0. 3, 0. 5, 0. 8, and 1. 0 are considered in our study. Based on the numerical outcomes, we find that the phase transitions for J₂/|J₁| = 0. 20, 0. 22, 0. 23, and 0. 24 are second order and are governed by the 2D Ising universality class. In addition, we find evidence to support the facts that there are transitions for J₂/|J₁| = 0. 5, 0. 8 and 1. 0 and these phase transitions are second order. Our results also indicate phase transition is unlikely to take place for g=0. 3. We are not able to obtain results for J₂/|J₁| (0. 24, 0. 3) because the associated integrated autocorrelation times or (and) the equilibrium times are extremely large at the low-temperature region. A comparison between the outcomes presented here and the available results in the literature is briefly conducted as well.