Lach M, Žukovič M
Institute of Physics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovakia.
Phys Rev E. 2020 Sep;102(3-1):032113. doi: 10.1103/PhysRevE.102.032113.
Critical properties of a geometrically frustrated generalized XY model with antiferromagnetic (AFM) and third-order antinematic (AN3) couplings on a triangular lattice are studied by Monte Carlo simulation. It is found that such a generalization leads to a phase diagram consisting of three different quasi-long-range ordered (QLRO) phases. Compared to the model with the second-order antinematic (AN2) coupling, besides the AFM and AN3 phases which appear in the limits of relatively strong AFM and AN3 interactions, respectively, it includes an additional complex canted antiferromagnetic (CAFM) phase. It emerges at lower temperatures, wedged between the AFM and AN3 phases as a result of the competition between the AFM and the AN3 couplings, which is absent in the model with the AN2 coupling. The AFM-CAFM and AN3-CAFM phase transitions are concluded to belong to the weak Ising and weak three-state Potts universality classes, respectively. Additionally, all three QLRO phases also feature true LRO of the standard and generalized chiralities, which both vanish simultaneously at second-order phase transitions with non-Ising critical exponents and the critical temperatures slightly higher than the magnetic and nematic order-disorder transition temperatures.
通过蒙特卡罗模拟研究了三角晶格上具有反铁磁（AFM）和三阶反运动学（AN3）耦合的几何受挫广义XY模型的临界性质。发现这种推广导致了一个由三个不同的准长程有序（QLRO）相组成的相图。与具有二阶反运动学（AN2）耦合的模型相比，除了分别出现在相对较强的AFM和AN3相互作用极限中的AFM和AN3相之外，它还包括一个额外的复杂倾斜反铁磁（CAFM）相。它在较低温度下出现，由于AFM和AN3耦合之间的竞争而夹在AFM和AN3相之间，这在具有AN2耦合的模型中不存在。得出AFM-CAFM和AN3-CAFM相变分别属于弱伊辛和弱三态Potts普适类。此外，所有三个QLRO相还具有标准和广义手性的真正长程有序（LRO），它们在具有非伊辛临界指数且临界温度略高于磁和向列序-无序转变温度的二阶相变中同时消失。
