Bonati Claudio, Pelissetto Andrea, Vicari Ettore
Dipartimento di Fisica dell'Università di Pisa and INFN Largo Pontecorvo 3, I-56127 Pisa, Italy.
Dipartimento di Fisica dell'Università di Roma Sapienza and INFN Sezione di Roma I, I-00185 Roma, Italy.
Phys Rev E. 2021 Jul;104(1-1):014140. doi: 10.1103/PhysRevE.104.014140.
We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP^{1} model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP^{1} gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case, the behavior is extremely sensitive to GSB perturbations.
我们研究了具有标量场的三维晶格规范理论中规范对称性破缺（GSB）微扰的影响。我们在规范关联不具有临界性且规范对称性仅选择变为临界的规范不变标量自由度的转变处研究此问题。实现这种行为的一个典型模型是晶格CP¹模型，或者更一般地，是具有双分量复标量场和紧致规范场的晶格阿贝尔 - 希格斯模型。我们考虑存在线性GSB微扰时的这个模型。结果表明，规范对称性对于GSB微扰相当稳健：即使存在有限的小GSB项，连续极限也是规范不变的。我们还确定了该模型的相图。它有一个无序相以及分别为张量有序和矢量有序的两个相。它们由属于O(3)、O(4)和O(2)矢量普适类的连续转变线分隔开，这些转变线在一个多临界点相交。我们注意到，CP¹规范对称临界点处的行为与规范关联变为临界的转变处的行为有很大不同，例如在由带电不动点控制的非紧致晶格阿贝尔 - 希格斯模型的转变中：在这种情况下，行为对GSB微扰极其敏感。
