Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917699240591360 |
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| author | Bonati, Claudio Pelissetto, Andrea Vicari, Ettore |
| author_facet | Bonati, Claudio Pelissetto, Andrea Vicari, Ettore |
| contents | 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 $v\not=0$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry Bonati, Claudio Pelissetto, Andrea Vicari, Ettore Statistical Mechanics High Energy Physics - Lattice 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 $v\not=0$, 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. |
| title | Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry |
| topic | Statistical Mechanics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2403.12758 |