Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory

Abstract

We investigate under which conditions the three-dimensional (3D) multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the continuum limit of statistical lattice gauge models, i.e., when it characterizes the universal behavior at critical transitions occurring in these models. We perform Monte Carlo simulations of the lattice AH model with compact gauge fields and Ncomponent scalar fields with charge q ≥ 2 for N = 15 and 25. Finite-size scaling analyses of the Monte Carlo data show that the transitions along the line separating the confined and deconfined phases are continuous and that they belong to the same universality class for any q ≥ 2. Moreover, they are in the same universality class as the transitions in the lattice AH model with noncompact gauge fields along the Coulomb-to-Higgs transition line. We finally argue that these critical behaviors are described by the stable charged fixed point of the renormalization-group flow of the 3D AH field theory.

Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement

“…37 , where an analogous discretization of the compact Abelian Higgs model with charge Q = 2 has been studied, since the presence of first order phase transitions can never be excluded by universality arguments alone. However, it will be surely interesting to understand, in future studies, the dynamical origin of this difference, to better understand the relation between the compact and the non-compact models [30][31][32] . In particular, it is still an open question whether transitions of the continuous Abelian Higgs universality class are possible in a lattice model with a finite Abelian gauge group, like the one studied in Ref.…”

“…At present we however know only few classical lattice models exhibiting this type of critical transitions: compelling evidence has been found for the multicomponent non-compact lattice Abelian Higgs model 30 and the multicomponent compact lattice Abelian Higgs model with charge Q ≥ 2 (see Refs. 31,32 ), while for non-Abelian gauge models we only have hints of this type of behavior 23,24 .…”

“…For the Abelian Higgs universality class we use the results obtained in Ref. 32 (see also Refs. 30,31 ); note that in this case the exponent η is not defined since the corresponding correlator is not gauge invariant and vanishes.…”

“…Examples of this behavior are found in the multicomponent non-compact lattice Abelian Higgs model [28][29][30] , in the multicomponent compact lattice Abelian Higgs model with charge Q ≥ 2 (see Refs. 31,32 ), and also in some non-Abelian models 23,34,35 .…”

“…37 , where a Z q deformation of the compact U(1) lattice Abelian Higgs model with charge Q = 2 (see Refs. 31,32 ) was investigated. By studying the region of the parameter space where transitions of the continuous Abelian Higgs universality class could emerge, the Authors found however only first order transitions for values of q up to q = 10.…”