Stability of fixed points and generalized critical behavior in multifield models

Abstract

We study models with three coupled vector fields characterized by $O(N_1)\oplus O(N_2)\oplus O(N_3)$ symmetry. Using the nonperturbative functional renormalization group, we derive $\beta$ functions for the couplings and anomalous dimensions in $d$ dimensions. Specializing to the case of three dimensions, we explore interacting fixed points that generalize the $O(N)$ Wilson-Fisher fixed point. We find a symmetry-enhanced isotropic fixed point, a large class of fixed points with partial symmetry enhancement, as well as partially and fully decoupled fixed point solutions. We discuss their stability properties for all values of $N_1,N_2$, and $N_3$, emphasizing important differences to the related two-field models. For small numbers of field components we find no stable fixed point solutions, and we argue that this can be attributed to the presence of a large class of possible (mixed) couplings in the three-field and multifield models. Furthermore, we contrast different mechanisms for stability interchange between fixed points in the case of the two- and three-field models, which generically proceed through fixed-point collisions.

14 pages, 15 figures; PRE version, minor changes

References in corpus (35)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• Critical Exponents of the N-vector model
• Optimised Renormalisation Group Flows
• Functional renormalization group approach to correlated fermion systems
• Fermi-Hubbard physics with atoms in an optical lattice
• Optimisation of the exact renormalisation group
• Quantum Einstein Gravity
• Critical Exponents from the Effective Average Action
• Derivative Expansion of the Exact Renormalization Group
• Fundamentals of the Exact Renormalization Group
• SO(5) Theory of Antiferromagnetism and Superconductivity
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Lectures on the functional renormalization group method
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Ising exponents from the functional renormalisation group
• Functional renormalization for spontaneous symmetry breaking in the Hubbard model
• Is there a Landau Pole Problem in QED?
• The critical behavior of frustrated spin models with noncollinear order
• Three dimensional massive scalar field theory and the derivative expansion of the renormalization group
• O(N)-Universality Classes and the Mermin-Wagner Theorem
• High-accuracy scaling exponents in the local potential approximation
• Multicritical behavior in models with two competing order parameters
• Fixed point stability and decay of correlations
• Randomly dilute Ising model: A nonperturbative approach
• Stability of Quantum Critical Points in the Presence of Competing Orders
• Comment on "Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory"
• Field theory of bi- and tetracritical points: Statics
• Properties of derivative expansion approximations to the renormalization group
• Triviality from the Exact Renormalization Group
• The derivative expansion of the renormalization group

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• The nonperturbative functional renormalization group and its applications
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• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Conformal Gauge-Yukawa Theories away From Four Dimensions
• Scaling relations and multicritical phenomena from Functional Renormalization
• Universal behavior of coupled order parameters below three dimensions
• Discovering and quantifying nontrivial fixed points in multi-field models
• Multi-fixed point numerical conformal bootstrap: a case study with structured global symmetry
• Phase diagram of Model C in the parametric space of order parameter and space dimensions