Phase transitions in the frustrated Ising model on the square lattice

We consider the thermal phase transition from a paramagnetic to a stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J₁0 (second neighbor, antiferromagnetic). The striped phase breaks a Z₄ symmetry and is stabilized at low temperatures for g=J₂/|J₁|>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. Phys. Rev. Lett. 108, 045702 (2012). Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J₁-J₂ model has a line of very weak first-order phase transitions in the whole region 1/21/2. Most of our conclusions are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.