$\u03bc(U)(1)^N$ 晶格 London 模型中的相变与复合序
Phase transitions and composite order in $\mathrm{U}(1)^N$ lattice London models
AI总结：
本研究定量考察U(1)^N晶格London模型中有序—无序相变随分量数N的变化，发现至少N≤7时为不连续相变，并揭示强耦合下中性与带电部分相变分离，在N>2时形成复合序新相；对偶分析表明有向环间范德华型作用可能驱动不连续性。
摘要：
具有 Abel 规范场的多分量规范理论的相图及相变性质是一个具有多种物理应用的重要课题。早期基于重整化群的研究表明，对于 $N = 1$ 和 $N > 183$，从完全有序态到完全无序态的直接相变是连续的，但最近的研究证明，当 $N = 2$ 时该相变是不连续的。我们定量研究了该相变不连续程度对 $N$ 的依赖关系。我们的结果表明，至少在 $N = 7$ 以内，该相变都是不连续的。此外，我们证明，在增大的耦合强度下，模型中中性部分和带电部分的相变会发生分离，对于 $N > 2$ 的情况，这会产生一个具有复合序的新相。从复合序相到完全无序相的相变同样是不连续的，至少在 $N = 3$ 和 $N = 4$ 时如此。通过对偶论证，这表明有向环之间的 van der Waals 型相互作用可能是这些模型中出现不连续相变的原因。
英文摘要：
The phase diagrams and the nature of the phase transitions in multicomponent gauge theories with an Abelian gauge field are important topics with various physical applications. While an early renormalization-group-based study indicated that the direct transition from a fully ordered to a fully disordered state is continuous for $N = 1$ and $N > 183$, recently it was demonstrated that the transition is discontinuous for $N = 2$. We quantitatively study the dependence on $N$ of the degree of discontinuity of this transition. Our results suggest that the transition is discontinuous at least up to $N = 7$. Furthermore, we demonstrate that, at increased coupling strength, the phase transitions of the neutral and charged sectors of the model split, which for $N > 2$ yields a new phase with composite order. The transition from the composite-order phase to the fully disordered phase is then also discontinuous, at least for $N = 3$ and $N = 4$. Via a duality argument, this indicates that van der Waals-type interaction between directed loops may be responsible for the discontinuous phase transitions in these models.
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