%0 Journal Article %1 Kalz2012Location %A Kalz, Ansgar %A Honecker, Andreas %D 2012 %J Physical Review B %K frustration, potts-model critical-phenomena lattice-models ising-model %N 13 %R 10.1103/PhysRevB.86.134410 %T Location of the Potts-critical end point in the frustrated Ising model on the square lattice %U http://dx.doi.org/10.1103/PhysRevB.86.134410 %V 86 %X 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.

@article{Kalz2012Location, 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 \et [PRL \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.}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Kalz, Ansgar and Honecker, Andreas}, biburl = {https://www.bibsonomy.org/bibtex/21847756fb24926799a34da4a84364033/nonancourt}, citeulike-article-id = {11238346}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevB.86.134410}, citeulike-linkout-1 = {http://arxiv.org/abs/1209.2265}, citeulike-linkout-2 = {http://arxiv.org/pdf/1209.2265}, day = 11, doi = {10.1103/PhysRevB.86.134410}, eprint = {1209.2265}, interhash = {69c6394b474e7e045420cabb9a60c5c2}, intrahash = {1847756fb24926799a34da4a84364033}, issn = {1550-235X}, journal = {Physical Review B}, keywords = {frustration, potts-model critical-phenomena lattice-models ising-model}, month = oct, number = 13, posted-at = {2012-09-17 10:40:13}, priority = {2}, timestamp = {2019-08-01T16:15:00.000+0200}, title = {{Location of the Potts-critical end point in the frustrated Ising model on the square lattice}}, url = {http://dx.doi.org/10.1103/PhysRevB.86.134410}, volume = 86, year = 2012 }