紧化空间坐标下（2+1）维模型中超导性与手征对称性破缺的相互作用
Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
摘要：
本文研究了一个具有四费米子相互作用的（2+1）维模型，其中一个空间坐标是紧化的，空间拓扑为无限圆柱$R^1\otimes S^1$ .假设系统嵌入实三维空间，磁通量$Φ$穿过圆柱体的横截面。该模型包括费米子-反费米子（或手征）和费米子-费米子（或超导）通道中的四费米子相互作用。然后，我们研究相变依赖于化学势$μ$和流量$Φ$的大- $N$展开技术，其中$N$是费米子场的数量的领先顺序。结果表明，对于手征通道和超导通道中耦合常数之间的任意关系，当$μ$值较高时（周长$S^1$的长度$L$是固定的），系统中出现超导性.此外，它示出，在足够小的值的$μ$的磁通量$Φ$的增长导致周期性再入的手征对称性打破或超导相，根据$μ$和耦合常数的值。
英文摘要：
In this paper a (2+1)-dimensional model with four-fermion interactions is investigated in the case when one spatial coordinate is compactified and the space topology takes the form of an infinite cylinder, $R^1\otimes S^1$. It is supposed that the system is embedded into real three-dimensional space and that a magnetic flux $Φ$ crosses the transverse section of the cylinder. The model includes four-fermion interactions both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels. We then study phase transitions in dependence on the chemical potential $μ$ and the flux $Φ$ in the leading order of the large-$N$ expansion technique, where $N$ is the number of fermion fields. It is demonstrated that for arbitrary relations between coupling constants in the chiral and superconducting channels, superconductivity appears in the system at rather high values of $μ$ (the length $L$ of the circumference $S^1$ is fixed). Moreover, it is shown that at sufficiently small values of $μ$ the growth of the magnetic flux $Φ$ leads to a periodical reentrance of the chiral symmetry breaking or superconducting phase, depending on the values of $μ$ and coupling constants.
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