Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged N-component scalar fields and SO(N) symmetry

We consider a three-dimensional lattice Abelian Higgs gauge model for a charged N-component scalar field phi, which is invariant under SO(N) global transformations for generic values of the parameters. We focus on the strong-coupling regime, in which the kinetic Hamiltonian term for the gauge field is a small perturbation, which is irrelevant for the critical behavior. The Hamiltonian depends on a parameter v, which determines the global symmetry of the model and the symmetry of the low-temperature phases. We present renormalization-group predictions, based on a Landau-Ginzburg-Wilson effective description that relies on the identification of the appropriate order parameter and on the symmetry-breaking patterns that occur at the strong-coupling phase transitions. For v = 0, the global symmetry group of the model is SU(N); the corresponding model may undergo continuous transitions only for N = 2. For v not equal 0, i.e., in the SO(N) symmetric case, continuous transitions (in the Heisenberg universality class) are possible also for N = 3 and 4. We perform Monte Carlo simulations for N = 2, 3, 4, 6, to verify the renormalization-group predictions. Finite-size scaling analyses of the numerical data are in full agreement.