Ashkin-Teller criticality and pseudo-first-order behavior in a frustrated Ising model on the square lattice

We consider the square-lattice frustrated Ising model with first- and second-neighbor interactions, $J_1<0$ and $J_2>0$. Its thermal phase transition to ``stripe'' order when $g=J_2/|J_1|>1/2$ has remained controversial despite many past studies. Using Monte Carlo simulations to investigate the order-parameter distribution and its Binder cumulant, we demonstrate Ashkin-Teller criticality for $g \ge g^*$, i.e., the critical exponents vary continuously between those of the $4$-state Potts model at $g^*$ and the Ising model for $g \to \infty$. The Potts point, below which the transition is first-order, is $g^*= 0.67 \pm 0.01$, much lower than previously believed. The system exhibits {\it pseudo first-order} behavior for $g^* \le g \le g^{\prime}\ (g^{\prime}\approx 0.9)$, which was previously misinterpreted as actual first-order behavior.