Abstract
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 non-critical 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 PRL 108, 045702 (2012) that
the transition point is at a value of \$J\_2/J\_1 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.
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