Three-dimensional antiferromagnetic CP(N-1) models

Abstract

We investigate the critical behavior of three-dimensional antiferromagnetic CP(N-1) [ACP(N-1)] models in cubic lattices, which are characterized by a global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-Ginzburg-Wilson (LGW) model. For N=3 this mapping allows us to conclude that the three-component ACP(2) model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP(2) and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N>3. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.

13 pages

References in corpus (27)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• Quantum Field Theory in the Large N Limit: a review
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Critical exponents for 3D O(n)-symmetric model with n > 3
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Relevance of the axial anomaly at the finite-temperature chiral transition in QCD
• N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Fate of CP(N-1) fixed points with q-monopoles
• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Critical behavior of O(2)xO(N) symmetric models
• Multicritical behavior in the fully frustrated XY model and related systems
• The order of the metal to superconductor transition
• 3D loop models and the CP^{n-1} sigma model
• Phase transitions in 3D loop models and the $C{P}^{n-1}$ $\sigma$ model
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Transitions and crossover phenomena in fully frustrated XY systems
• The finite-temperature chiral transition in QCD with adjoint fermions
• The normal-to-planar superfluid transition in Helium 3
• Numerical study of the enlarged O(5) symmetry of the 3-D antiferromagnetic RP2 spin model
• Effective field theory for Sp(N) antiferromagnets and its phase structure
• Third-harmonic exponent in three-dimensional N-vector models
• Phase diagram of the (bosonic) Double-Exchange Model

Cited by in corpus (22)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Lattice Abelian-Higgs model with noncompact gauge fields
• Multicomponent compact Abelian-Higgs lattice models
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Three-dimensional ferromagnetic CP(N-1) models
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Criticality of O(N) symmetric models in the presence of discrete gauge symmetries
• Matrix models at large charge
• Bootstrapping traceless symmetric $O(N)$ scalars
• Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories
• Landau-Ginzburg-Wilson approach to critical phenomena in the presence of gauge symmetries
• Exploring $SU(N)$ adjoint correlators in $3d$
• Nonperturbative infrared finiteness in super-renormalisable scalar quantum field theory
• Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• A matrix CFT at multiple large charges
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Critical points in the $C{P}^{N-1}$ model
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality