二维格子标量色动力学的普适低温行为
Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics
摘要：
我们研究的作用，全球和当地的非交换对称性在二维格点规范理论与多组分标量场。我们从一个最大O（$M$）对称的多组分标量模型出发，对其对称性进行部分规范化，得到了具有整体U $(N_f)$（对于$N_c\ge 3$）或Sp（$N_f$）对称性（对于$N_c=2$）的SU（$N_c$）规范理论（标量色动力学），其中$N_f>1$是味数.相应地，这些域属于陪集$S^M$ /SU（$N_c$），其中$S^M$是$M$维球面，而$M=2 N_f N_c$是.与Mermin-Wagner定理一致，系统在有限温度下总是无序的，并且临界行为仅在零温度极限下发展。它的通用功能进行了研究的数值有限尺寸标度方法。结果表明，低温下的渐近行为属于二维CP $N_c>2$场论的普适类，而属于二维Sp（$N_f$）场论的普适类，对于$N_c=2$ .这些普适性类对应于与对称空间相关的二维统计场论，这些对称空间对于$N_c=2$在Sp（$N_f$）变换下是不变的，对于$N_c > 2$在SU（$N_f$）变换下是不变的。这些对称群与标量色动力学的不变性群是相同的，除了$N_f \ge N_c > 2$存在的U（1）味对称，它在确定模型的渐近行为中不起任何作用。
英文摘要：
We study the role that global and local nonabelian symmetries play in two-dimensional lattice gauge theories with multicomponent scalar fields. We start from a maximally O($M$)-symmetric multicomponent scalar model, Its symmetry is partially gauged to obtain an SU($N_c$) gauge theory (scalar chromodynamics) with global U$(N_f)$ (for $N_c\ge 3$) or Sp($N_f$) symmetry (for $N_c=2$), where $N_f>1$ is the number of flavors. Correspondingly, the fields belong to the coset $S^M$/SU($N_c$) where $S^M$ is the $M$-dimensional sphere and $M=2 N_f N_c$. In agreement with the Mermin-Wagner theorem, the system is always disordered at finite temperature and a critical behavior only develops in the zero-temperature limit. Its universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the 2D CP$^{N_f-1}$ field theory for $N_c>2$, and to that of the 2D Sp($N_f$) field theory for $N_c=2$. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp($N_f$) transformations for $N_c=2$ and under SU($N_f$) for $N_c > 2$. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for $N_f \ge N_c > 2$, which does not play any role in determining the asymptotic behavior of the model.
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