Multicritical behavior in models with two competing order parameters

Abstract

We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N_1, N_2 plane. We study the fate of non-trivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of non-canonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.

arXiv comment16 pages, 7 figures, 5 tables, minor changes in updated version, identical to published one in Phys. Rev. E

References in corpus (80)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Exact evolution equation for the effective potential
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• 2D Gravity and Random Matrices
• Hybrid Inflation
• Nonperturbative Evolution Equation for Quantum Gravity
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• Functional renormalization group approach to correlated fermion systems
• Riemannian symmetric superspaces and their origin in random matrix theory
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Inflationary Cosmology
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Asymptotic safety of gravity and the Higgs boson mass
• Critical behavior of the three-dimensional XY universality class
• An Introduction to the Nonperturbative Renormalization Group
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Quark Confinement from Color Confinement
• The critical exponents of the superfluid transition in He4
• Lectures on the functional renormalization group method
• The Phase Diagram of the Quark-Meson Model
• Asymptotic Safety of Gravity Coupled to Matter
• Critical exponents from optimised renormalisation group flows
• On the relation of quark confinement and chiral symmetry breaking
• Absence of supersolidity in solid helium in porous Vycor glass
• Nonperturbative renormalization group approach to frustrated magnets
• Contraints on Matter from Asymptotic Safety
• 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
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Effective Action for the Quark-Meson Model
• Renormalization Group Flow in Scalar-Tensor Theories. I
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• QED coupled to QEG
• Asymptotic freedom of Yang-Mills theory with gravity
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Gravitational corrections to Yukawa systems
• Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
• Quark-meson-diquark model for two-color QCD
• Light fermions in quantum gravity
• Ising exponents from the functional renormalisation group
• Running Gauge Coupling in Asymptotically Safe Quantum Gravity
• Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario
• Heisenberg frustrated magnets: a nonperturbative approach
• Phase transition and critical behaviour of the d=3 Gross-Neveu model
• Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$
• Critical exponents of the Gross-Neveu model from the effective average action
• The Renormalization Group and Two Dimensional Multicritical Effective Scalar Field Theory
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter
• O(N)-Universality Classes and the Mermin-Wagner Theorem
• Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ${\epsilon }^{1/2}$-Expansion
• Critical behavior of the (2+1)-dimensional Thirring model
• Ultracold atoms and the Functional Renormalization Group
• Renormalization Group Flow in Scalar-Tensor Theories. II
• Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems
• Functional renormalization group approach to the BCS-BEC crossover
• Asymptotic safety of simple Yukawa systems
• Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model
• Projected SO(5) Models
• Five-loop \sqrtε-expansions for random Ising model and marginal spin dimensionality for cubic systems
• Equation of state and coarse grained free energy for matrix models
• Randomly dilute Ising model: A nonperturbative approach
• Stability of a cubic fixed point in three dimensions. Critical exponents for generic N
• Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene
• Comment on "Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory"
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• The stability of the O(N) invariant fixed point in three dimensions
• Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations
• Coleman-Weinberg Phase Transition in Two-Scalar Models
• High Temperature Phase Transition in Two-Scalar Theories
• Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory
• Field theory of bi- and tetracritical points: Statics
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Fermions and Goldstone bosons in an asymptotically safe model
• Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic field
• Evidence for a bicritical point in the XXZ Heisenberg antiferromagnet on a simple cubic lattice
• Functional Renormalization of Noncommutative Scalar Field Theory
• The stability of a cubic fixed point in three dimensions from the renormalization group

Cited by in corpus (46)

• The nonperturbative functional renormalization group and its applications
• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Nematic superconductivity in twisted bilayer graphene
• Quantum phases of SrCu2(BO3)2 from high-pressure thermodynamics
• Zooming in on fermions and quantum gravity
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly
• Strain-induced time-reversal odd superconductivity in graphene
• Lee-Yang model from the functional renormalization group
• Non-equilibrium fixed points of coupled Ising models
• Fractal dimension of critical curves in the $O(n)$-symmetric ${\varphi }^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Mott multicriticality of Dirac electrons in graphene
• Critical $O(N)$ models in the complex field plane
• Critical temperature and superfluid gap of the Unitary Fermi Gas from Functional Renormalization
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• A functional perspective on emergent supersymmetry
• Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
• 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
• Emergent symmetries and coexisting orders in Dirac fermion systems
• The phase diagram of the underdoped cuprates at high magnetic field
• Critical phenomena at the complex tensor ordering phase transition
• Discovering and quantifying nontrivial fixed points in multi-field models
• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking
• Stability of fixed points and generalized critical behavior in multifield models
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Critical and multicritical behavior in the Ising-Heisenberg universality class
• Infinite distances in multicritical CFTs and higher-spin holography
• Emergent ${\mathbb{Z}}_2$ symmetry near a CDW multicritical point
• Ising-XY Transition in Three-dimensional Frustrated Antiferromagnets with Collinear Ordering
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Quantum phase transitions in a bidimensional $O(N)\times {\mathbb{Z}}_2$ scalar field model
• Nonperturbative Renormalization Group for the Landau-de Gennes Model
• Anisotropic XY antiferromagnets in a field
• Charged and neutral fixed points in the O(N)+O(N)-model with Abelian gauge fields
• Finite size effects in the phase transition patterns of coupled scalar field systems
• 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
• Control, competition and coexistence of effective magnetic orders by interactions in Bose-Einstein condensates with high-Q cavities