论文标题
带有非相对量规场的晶格Abelian-Higgs模型
Lattice Abelian-Higgs model with noncompact gauge fields
论文作者
论文摘要
我们考虑具有$ n $组成的复杂标量字段的三维电动力学的非划定晶格公式，即带有非相对规格场的晶格Abelian-Higgs模型。 For any $N\ge 2$, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: the Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalar-field and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations).它们通过在多政治点上的三个过渡线隔开。它们的性质取决于共存的阶段以及标量字段的组成部分的数字$ n $。特别是，库仑至分子过渡线（仪表相关性无关）与Landau-Ginzburg-Wilson $φ^4 $理论共享相同的SU（$ n $）全球对称性，但没有明确的仪表字段。另一方面，库仑到木的过渡线（相关规格相关性）证明了具有显式量规场的连续体亚伯·希格斯田间理论。我们的数值研究基于具有$ C^*$边界条件的蒙特卡洛模拟的有限尺寸缩放分析（适用于具有非2级变量的晶格系统，与周期性边界条件不同），对于$ n $，即$ n = 2，4，4，10，15 $和$ 25 $的几个值。数值结果与连续性场理论的重新归一化组预测一致。尤其是，库仑到希格斯的过渡对于$ n \ gtrsim 10 $是连续的，这与阿贝利安·希格斯田间理论的预测一致。
We consider a noncompact lattice formulation of the three-dimensional electrodynamics with $N$-component complex scalar fields, i.e., the lattice Abelian-Higgs model with noncompact gauge fields. For any $N\ge 2$, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: the Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalar-field and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the coexisting phases and on the number $N$ of components of the scalar field. In particular, the Coulomb-to-molecular transition line (where gauge correlations are irrelevant) is associated with the Landau-Ginzburg-Wilson $Φ^4$ theory sharing the same SU($N$) global symmetry but without explicit gauge fields. On the other hand, the Coulomb-to-Higgs transition line (where gauge correlations are relevant) turns out to be described by the continuum Abelian-Higgs field theory with explicit gauge fields. Our numerical study is based on finite-size scaling analyses of Monte Carlo simulations with $C^*$ boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of $N$, i.e., $N=2, 4, 10, 15$, and $25$. The numerical results agree with the renormalization-group predictions of the continuum field theories. In particular, the Coulomb-to-Higgs transitions are continuous for $N\gtrsim 10$, in agreement with the predictions of the Abelian-Higgs field theory.
