A Comprehensive Study of the Phase Transitions of the Frustrated J₁-J₂ Ising Model on the Square Lattice

We study the phase transitions of the two-dimensional (2D) frustrated J₁-J₂ Ising model on the square lattice with Monte Carlo simulations. Here J₁ < 0 and J₂ > 0 are the couplings for the nearest and next nearest neighbor Ising spins, respectively. In addition, we consider J₁ = −1 and J₂/|J₁| ≡ g = 0.56, 0.58, 0.60, 0.62, 0.64, and 0.7 in our investigation. Several physical quantities including the Binder ratio U, the specific heat C_v, and the energy density E are obtained. The analyses of these calculated observables indicate that the considered phase transitions for g ≥ 0.58 are likely second order, and the nature of the phase transition associated with g = 0.56 needs further investigation. A comparison between the histograms of E for the phase transitions considered here and the one associated with the five-state ferromagnetic Potts model on the square lattice is conducted. The outcomes imply that if the studied phase transitions are weakly first order, then they have much larger correlation lengths than that of the five-state Potts model.