Analysis of the phase transition for the Ising model on the frustrated square lattice

We analyze the phase transition of the frustrated $J_1$-$J_2$ Ising model with antiferromagnetic nearest- and strong next-nearest neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for $1/2 < J_2/J_1 \lesssim 1$ is not of the weakly universal type -- as commonly believed -- but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models ($J_1 = 0$), we calculate the effect of the nearest neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.