We consider three-dimensional lattice SU($N_c$) gauge theories with multiflavor ($N_f>1$) scalar fields in the adjoint representation. We investigate their phase diagram, identify the different Higgs phases with their gauge-symmetry pattern, and dete
rmine the nature of the transition lines. In particular, we study the role played by the quartic scalar potential and by the gauge-group representation in determining the Higgs phases and the global and gauge symmetry-breaking patterns characterizing the different transitions. The general arguments are confirmed by numerical analyses of Monte Carlo results for two representative models that are expected to have qualitatively different phase diagrams and Higgs phases. We consider the model with $N_c = 3$, $N_f=2$ and with $N_c=2$, $N_f= 4$. This second case is interesting phenomenologically to describe some features of cuprate superconductors.
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 th
e 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.
We study perturbations that break gauge symmetries in lattice gauge theories. As a paradigmatic model, we consider the three-dimensional Abelian-Higgs (AH) model with an N-component scalar field and a noncompact gauge field, which is invariant under
U(1) gauge and SU(N) transformations. We consider gauge-symmetry breaking perturbations that are quadratic in the gauge field, such as a photon mass term, and determine their effect on the critical behavior of the gauge-invariant model, focusing mainly on the continuous transitions associated with the charged fixed point of the AH field theory. We discuss their relevance and compute the (gauge-dependent) exponents that parametrize the departure from the critical behavior (continuum limit) of the gauge-invariant model. We also address the critical behavior of lattice AH models with broken gauge symmetry, showing an effective enlargement of the global symmetry, from U(N) to O(2N), which reflects a peculiar cyclic renormalization-group flow in the space of the lattice AH parameters and of the photon mass.
We consider two-dimensional lattice SU($N_c$) gauge theories with $N_f$ real scalar fields transforming in the adjoint representation of the gauge group and with a global O($N_f$) invariance. Focusing on systems with $N_fge 3$, we study their zero-te
mperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a $sigma$ model defined on a symmetric space that has the same global symmetry as the lattice model.
We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) s
ymmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N>1 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement/deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly-charged unit-length scalar fields with small and large number of components, i.e. N=2 and N=25.
We study the phase diagram and critical behavior of a two-dimensional lattice SO($N_c$) gauge theory ($N_c ge 3$) with two scalar flavors, obtained by partially gauging a maximally O($2N_c$) symmetric scalar model. The model is invariant under local
SO($N_c$) and global O(2) transformations. We show that, for any $N_c ge 3$, it undergoes finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with the global Abelian O(2) symmetry. The transition separates a high-temperature disordered phase from a low-temperature spin-wave phase where correlations decay algebraically (quasi-long range order). The critical properties at the finite-temperature BKT transition and in the low-temperature spin-wave phase are determined by means of a finite-size scaling analysis of Monte Carlo data.
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 $Nge 2$, 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 $Phi^4$ 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 $Ngtrsim 10$, in agreement with the predictions of the Abelian-Higgs field theory.
We address the interplay between global and local gauge nonabelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar nonabelian gauge theories with a local SO(Nc) (Nc >= 3) and a global
O(Nf) invariance, obtained by partially gauging a maximally O(Nf x Nc)-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset S(Nf Nc-1)/SO(Nc), where S(N) is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SO(Nc) gauge models with Nf >= 3 do not have finite-temperature transitions related to the breaking of the global nonabelian O(Nf) symmetry. However, in the zero-temperature limit they show a critical behavior characterized by a correlation length that increases exponentially with the inverse temperature, similarly to nonlinear O(N) sigma models. Their 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 two-dimensional RP(Nf-1) model.
We investigate the low-temperature behavior of two-dimensional (2D) RP$^{N-1}$ models, characterized by a global O($N$) symmetry and a local ${mathbb Z}_2$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice models: tw
o standard lattice models and two different constrained models. We also consider a constrained mixed O(3)-RP$^2$ model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) $sigma$ model, suggesting the existence of a distinct 2D RP$^2$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an RP$^3$ universality class, different from the O(4) one.
We study the nature of the phase diagram of three-dimensional lattice models in the presence of nonabelian gauge symmetries. In particular, we consider a paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with N_f flavors, char
acterized by a nonabelian SU(N_c) gauge symmetry. For N_f>1 (multiflavor case), it presents two phases separated by a transition line where a gauge-invariant order parameter condenses, being associated with the breaking of the residual global symmetry after gauging. The nature of the phase transition line is discussed within two field-theoretical approaches, the continuum scalar chromodynamics and the Landau-Ginzburg- Wilson (LGW) Phi4 approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for N_f=2, 3 and N_c = 2, 3, and 4. The LGW approach turns out to provide the correct picture of the critical behavior, unlike continuum scalar chromodynamics.
