标题： 二维O(2)和O(3)主手性模型中畴壁和涡旋的相互作用 显示英文标题

标题： Interaction of domain walls and vortices in the two-dimensional O(2) and O(3) principal chiral models

摘要： 通过大量的蒙特卡洛模拟，我们研究了伊辛-$O(2)$模型和伊辛-$O(3)\otimes O(2)$模型中域壁、涡旋和$\mathbb{Z}_2$涡旋的临界性质。 我们考虑了当伊辛序参数中的无序在连续参数中引起无序的非平凡情况。 这种情况发生在域壁对连续参数相关性变得不透明时。 我们发现，在这种情况下，BKT相变（或交叉）点处的涡旋密度是非普适的，而在伊辛相变处的壁密度保持普适，即与伊辛模型一致。 本研究的重要部分是对缺陷-缺陷关联函数的数值测量。 我们发现，在伊辛点，壁-涡旋关联函数在热力学极限下趋于零，这解释了壁密度的普适性。 还讨论了这些模型可能的多临界行为。 显示英文摘要

摘要： Using extensive Monte Carlo simulations, we investigate the critical properties of domain walls, vortices and $\mathbb{Z}_2$ vortices in the Ising-$O(2)$ and Ising-$O(3)\otimes O(2)$ models. We have consider the nontrivial case when disorder in the Ising order parameter induces disorder in the continuous parameter. Such a situation arises when a domain wall becomes opaque for continuous parameter correlations. We find that in this case the vortex density at the BKT transition (or crossover) point turns out to be non-universal, while the wall density at the Ising transition remains universal, i.e. in agreement with the Ising model. An important part of this study is the numerical measurement of defect-defect correlators. We find that the wall-vortex correlator tends to zero in the thermodynamic limit at the Ising point, which explains the universality of the wall density. A possible multicritical behavior of the models is also discussed.