Competing interactions and the Lifshitz-type Nonlinear Sigma Model
arXiv:1305.3792 · doi:10.1103/PhysRevD.88.025050
Abstract
We establish the equivalence between the continuum limit of the quantum spherical model with competing interactions, which is relevant to the investigation of Lifshitz points, and the O(N) nonlinear sigma model with the addition of higher order spatial derivative operators, which breaks the Lorentz symmetry and is known as Lifshitz-type (or anisotropic) nonlinear sigma model. In the context of the 1/N expansion, we also discuss the renormalization properties of this nonlinear sigma model and find the nontrivial fixed points of the beta-functions in various dimensions, which turn out to be connected with the existence of phase transitions in the quantum spherical model.
29 pages, 9 figures. Clarifications added. Published version
References in corpus (6)
- Quantum Gravity at a Lifshitz Point
- Renormalization of Lorentz violating theories
- Renormalization group in Lifshitz-type theories
- Quantum spherical model with competing interactions
- Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point
- Supersymmetric Extension of the Quantum Spherical Model
Cited by in corpus (16)
- On the Horava-Lifshitz-like Gross-Neveu model
- Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
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- Lindblad dynamics of a quantum spherical spin
- Tree-Level Unitarity and Renormalizability in Lifshitz Scalar Theory
- On one-loop corrections in the Horava-Lifshitz-like QED
- Asymptotically free lattice gauge theory in five dimensions
- On the radiative corrections in the Horava-Lifshitz z=2 QED
- Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models
- Renormalization of Supersymmetric Lifshitz Sigma Models
- An UV Completion of Five Dimensional Scalar QED and Lorentz Symmetry
- Quantum Spherical Spins with Local Symmetry
- Spontaneous Symmetry Breaking and Frustrated Phases
- Supersymmetric Quantum Spherical Spins with Short-Range Interactions
- Tree-Unitarity and renormalizability in Lifshitz-scaling theory -- as a toy model of Hořava's gravity theory
- Supersymmetric Quantum Spherical Spins