Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional systems with internal symmetries
Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional systems with internal symmetries
复制标题
具有内部对称性的二维系统中的 Berezinskii-Kosterlitz-Thouless 相变
DOI：
10.1134/1.559059
复制
发表时间：
1999
影响因子：
1.1
通讯作者：
S. A. Bulgadaev
中科院分区：
文献类型：
--
作者：
S. A. Bulgadaev
摘要研究了具有内连续Abelian对称性的二维系统的Berezinskii-Kosterlitz-Thouless相变。为了使相变发生，系统的运动部分必须具有保形不变性，真空流形必须简并并具有离散阿贝尔同伦群π1。在这种情况下，拓扑激励具有对数发散的能量，可以用推广二维欧几里得正弦-戈登理论的有效理论来描述，这是原始XY模型的有效理论。特别地，我们发现了简单紧李群g的极大阿贝尔环面TG上的手性模型的有效作用。我们发现了可能的有效理论的临界性质，并证明了它们的晶格的Coxeter数hG是它们的特征
$$\mathbb{A},\mathbb{D},\mathbb{E}$$
并可解释为中心电荷为整数C=n的共形理论的性质，其中n为π1和G群的秩。本文还讨论了在质量相中重建G的完全对称性的可能性。
AbstractThe Berezinskii-Kosterlitz-Thouless (BKT) phase transitions in two-dimensional systems with internal continuous Abelian symmetries are investigated. In order for phase transitions to occur, the kinetic part of the action of the system must have conformal invariance, and the vacuum manifold must be degenerate and have a discrete Abelian homotopy group π1. In this case topological excitations have a logarithmically divergent energy and can be described by effective theories that generalize the two-dimensional Euclidean sine-Gordon theory, which is an effective theory of the original XY model. In particular, the effective actions are found for chiral models on the maximal Abelian tori TG of the simple compact Lie groups G. The critical properties of the possible effective theories are found, and it is shown that they are characterized by the Coxeter numbers hG of lattices of the
$$\mathbb{A},\mathbb{D},\mathbb{E}$$
and ℤ series and can be interpreted as properties of conformal theories with an integer central charge C=n, where n is the rank of the groups π1 and G. The possibility of reconstructing the complete symmetry of G in the massive phase is also discussed.