Three-dimensional antiferromagnetic CP(N-1) models

Nonperturbative Infrared Finiteness in a Superrenormalizable Scalar Quantum Field Theory

We present a study of the IR behavior of a three-dimensional superrenormalizable quantum field theory consisting of a scalar field in the adjoint of SU(N) with a φ^{4} interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory, the critical mass is ambiguous due to IR divergences, and we indeed find that at two loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [R. Jackiw et al., Phys. Rev. D 23, 2291 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2291, T. Appelquist et al., Phys. Rev. D 23, 2305 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2305] that superrenormalizable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov Chain Monte Carlo simulations of the lattice-regularized theory, frequentist and Bayesian data analysis, and considerations of a corresponding effective theory, we gather evidence that this is indeed the case.

Higher-charge three-dimensional compact lattice Abelian-Higgs models

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) symmetries. 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≥2 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 and 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.

Three-dimensional phase transitions in multiflavor lattice scalar SO(N_{c}) gauge theories

We investigate the phase diagram and finite-temperature transitions of three-dimensional scalar SO(N_{c}) gauge theories with N_{f}≥2 scalar flavors. These models are constructed starting from a maximally O(N)-symmetric multicomponent scalar model (N=N_{c}N_{f}), whose symmetry is partially gauged to obtain an SO(N_{c}) gauge theory, with O(N_{f}) or U(N_{f}) global symmetry for N_{c}≥3 or N_{c}=2, respectively. These systems undergo finite-temperature transitions, where the global symmetry is broken. Their nature is discussed using the Landau-Ginzburg-Wilson (LGW) approach, based on a gauge-invariant order parameter, and the continuum scalar SO(N_{c}) gauge theory. The LGW approach predicts that the transition is of first order for N_{f}≥3. For N_{f}=2 the transition is predicted to be continuous: It belongs to the O(3) vector universality class for N_{c}=2 and to the XY universality class for any N_{c}≥3. We perform numerical simulations for N_{c}=3 and N_{f}=2,3. The numerical results are in agreement with the LGW predictions.

Phase Diagram, Symmetry Breaking, and Critical Behavior of Three-Dimensional Lattice Multiflavor Scalar Chromodynamics

We study the nature of the phase diagram of three-dimensional lattice models in the presence of non-Abelian gauge symmetries. In particular, we consider a paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with N_{f} flavors, characterized by a non-Abelian SU(N_{c}) gauge symmetry. For N_{f}≥2 (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) Φ^{4} approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for N_{f}=2, 3 and N_{c}=2-4. The LGW approach turns out to provide the correct picture of the critical behavior at the transitions between the two phases.

Multicomponent compact Abelian-Higgs lattice models

We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_{x}^{a} of unit length and charge is coupled to compact quantum electrodynamics in the usual Wilson lattice formulation. We determine the phase diagram and study the nature of the transition line for N=2 and N=4. Two phases are identified, specified by the behavior of the gauge-invariant local composite operator Q_{x}^{ab}=z[over ¯]_{x}^{a}z_{x}^{b}-δ^{ab}/N, which plays the role of order parameter. In one phase, we have 〈Q_{x}^{ab}〉=0, while in the other Q_{x}^{ab} condenses. Gauge correlations are never critical: gauge excitations are massive for any finite coupling. The two phases are separated by a transition line. Our numerical data are consistent with the simple scenario in which the nature of the transition is independent of the gauge coupling. Therefore, for any finite positive value of the gauge coupling, we predict a continuous transition in the Heisenberg universality class for N=2 and a first-order transition for N=4. However, notable crossover phenomena emerge for large gauge couplings, when gauge fluctuations are suppressed. Such crossover phenomena are related to the unstable O(2N) fixed point, describing the behavior of the model in the infinite gauge-coupling limit.

Three-dimensional ferromagnetic CP^{N-1} models

We investigate the critical behavior of three-dimensional ferromagnetic CP^{N-1} models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we find a critical transition in the Heisenberg O(3) universality class, while for N=3 and 4 the system undergoes a first-order transition. For N=3 the transition is very weak and a clear signature of its discontinuous nature is only observed for sizes L≳50. We also determine the critical behavior for a large class of lattice Hamiltonians in the large-N limit. The results confirm the existence of a stable large-NCP^{N-1} fixed point. However, this evidence contradicts the standard picture obtained in the Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter: The presence of a cubic term in the effective LGW field theory for any N≥3 would usually be taken as an indication that these models generically undergo first-order transitions.

Criticality of O(N) symmetric models in the presence of discrete gauge symmetries

We investigate the critical properties of the three-dimensional antiferromagnetic RP^{N-1} model, which is characterized by a global O(N) symmetry and a discrete Z_{2} gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general Φ^{4} theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_{2} gauge symmetry.