Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovakia.
Phys Rev E. 2018 May;97(5-1):052101. doi: 10.1103/PhysRevE.97.052101.
Critical properties of the two-dimensional XY model involving solely nematic-like terms of the second and third orders are investigated by spin-wave analysis and Monte Carlo simulation. It is found that, even though neither of the nematic-like terms alone can induce magnetic ordering, their coexistence and competition leads to an extended phase of the magnetic quasi-long-range-order phase, wedged between the two nematic-like phases induced by the respective couplings. Thus, except for the multicritical point, at which all the phases meet, for any finite value of the coupling parameters ratio there are two phase transition: one from the paramagnetic phase to one of the two nematic-like phases followed by another one at lower temperatures to the magnetic phase. The finite-size scaling analysis indicates that the phase transitions between the magnetic and nematic-like phases belong to the Ising and three-state Potts universality classes. Inside the competition-induced algebraic magnetic phase, the spin-pair correlation function is found to decay even much more slowly than in the standard XY model with purely magnetic interactions. Such a magnetic phase is characterized by an extremely low vortex-antivortex pair density attaining a minimum close to the point at which the two couplings are of about equal strength.
通过自旋波分析和蒙特卡罗模拟研究了仅包含二阶和三阶向列相似项的二维 XY 模型的临界性质。研究发现，尽管单独的向列相似项都不能诱导磁有序，但它们的共存和竞争导致了磁准长程序相的扩展相，夹在由各自耦合诱导的两个向列相似相中。因此，除了所有相相遇的多临界点外，对于任何有限的耦合参数比值，都存在两个相转变：一个从顺磁相到两个向列相似相之一，然后在较低温度下到磁相。有限大小标度分析表明，磁相和向列相似相之间的相变属于伊辛和三态 Potts 普遍类。在竞争诱导的代数磁相中，自旋对相关函数的衰减速度甚至比具有纯磁相互作用的标准 XY 模型还要慢得多。这种磁相的特征是涡旋-反涡旋对密度极低，在接近两个耦合强度大致相等的点时达到最小值。
