Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged N-component scalar fields and SO(N) symmetry
arxiv(2024)
摘要
We consider a three-dimensional lattice Abelian Higgs gauge model for a
charged N-component scalar field ϕ, 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≠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.
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