Location of the Potts-critical end point in the frustrated Ising model on the square lattice

We report on Monte Carlo simulations for the two-dimensional frustrated $J_1$-$J_2$ Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear state different phase-transition scenarios apply depending on the value of the frustration $J_2 / J_1$. In particular a region with critical Ashkin-Teller-like behavior, i.e., a second-order phase transition with varying critical exponents, and a noncritical region with first-order indications were verified. However, the exact transition point $[J_2/J_1]_C$ between both scenarios was under debate. In this paper we present Monte Carlo data which strengthens the conclusion of Jin \et [Phys. Rev. Lett. \textbf{108}, 045702 (2012)] that the transition point is at a value of $J_2/J_1 \approx 0.67$ and that double-peak structures in the energy histograms for larger values of $J_2/J_1$ are unstable in a scaling analysis.