标题： 广义的$XY$模型，具有竞争的反铁磁和反向列相互作用 显示英文标题

标题： Generalized $XY$ model with competing antiferromagnetic and antinematic interactions

摘要： 我们研究$q$阶反向列（AN$_q$）相互作用对反铁磁（AF）$XY$模型在正方形晶格上的临界行为的影响。 发现这种AF-AN$_q$模型随着参数$q$的演化，其相图拓扑结构并不遵循与相应FM-N$_q$模型相同的规律，这些模型具有铁磁（FM）和$q$-阶向列（N$_q$）相互作用。它们的相图仅在参数$q$为奇数值时才相似。 在这些情况下，FM-N$_q$模型中报告的相应相位在AF-AN$_q$模型中分别出现在两个AF耦合子晶格上，相应的相变被认定为同一种类型。 另一方面，对于$q$的偶数值，AF-AN$_q$模型的相图与 FM-N$_q$模型不同，且其拓扑结构不随$q$变化。 除了在较高温度下在主导各自耦合区域观察到的纯AF和AN$_q$相外，在低温下存在一种新的倾斜（C）AF相，这是由AF和AN$_q$倾向之间的竞争引起的，并且在FM-N$_q$模型中没有对应相。 从AF和AN$_q$相到CAF相的相变似乎具有BKT特性。 显示英文摘要

摘要： We study effects of $q$-order antinematic (AN$_q$) interactions on the critical behavior of the antiferromagnetic (AF) $XY$ model on a square lattice. It is found that the evolution of the phase diagram topology of such AF-AN$_q$ models with the parameter $q$ does not follow the same line as for the corresponding FM-N$_q$ models with the ferromagnetic (FM) and $q$-order nematic (N$_q$) interactions. Their phase diagrams are similar only for odd values of the parameter $q$. In such cases the respective phases reported in the FM-N$_q$ models are observed in the AF-AN$_q$ models on each of the two AF-coupled sublattices and the corresponding phase transitions are concluded to be of the same kind. On the other hand, for even values of $q$ the phase diagrams of the AF-AN$_q$ models are different from the FM-N$_q$ models and their topology does not change with $q$. Besides the pure AF and AN$_q$ phases, observed at higher temperatures in the regions of the dominant respective couplings, at low temperatures there is a new canted (C)AF phase, which results from the competition between the AF and AN$_q$ ordering tendencies and has no counterpart in the FM-N$_q$ model. The phase transitions to the CAF phase from both AF and AN$_q$ phases appear to be of the BKT nature.