Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

Abstract

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N=2,3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.

arXiv comment4 pages, 5 figures. Discussion enlarged

References in corpus (20)

• Critical Phenomena and Renormalization-Group Theory
• Universality of phase transitions of frustrated antiferromagnets
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Two phase transitions in the fully frustrated $XY$ model
• Heisenberg frustrated magnets: a nonperturbative approach
• Randomly dilute spin models: a six-loop field-theoretic study
• The critical behavior of frustrated spin models with noncollinear order
• Phase transitions in anisotropic superconducting and magnetic systems with vector order parameters: Three-loop renormalization-group analysis
• Critical Exponents of the Fully Frustrated 2-D Xy Model
• Large-n Critical Behavior of O(n)xO(m) Spin Models
• Chiral transitions in three-dimensional magnets and higher order ε-expansion
• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
• Monte Carlo study of the Villain version of the fully frustrated XY model
• A non perturbative approach of the principal chiral model between two and four dimensions
• Chiral exponents in frustrated spin models with noncollinear ordering
• Comment on "Two Phase Transitions in the Fully frustrated XY Model"
• Non-equilibrium transitions in fully frustrated Josephson junction arrays
• Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group
• The fully frustrated XY model with next nearest neighbor interaction
• The critical behavior of 2-d frustrated spin models with noncollinear order

Cited by in corpus (41)

• The nonperturbative functional renormalization group and its applications
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Nonperturbative renormalization group approach to frustrated magnets
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Coherent and dissipative dynamics at quantum phase transitions
• Critical behavior of O(2)xO(N) symmetric models
• Criticality in quantum triangular antiferromagnets via fermionized vortices
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• XY frustrated systems: continuous exponents in discontinuous phase transitions
• Divergent Perturbation Series
• Fixed point stability and decay of correlations
• Five-loop epsilon expansion for O(n)xO(m) spin models
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Five-loop epsilon expansion for U(n)xU(m) models: finite-temperature phase transition in light QCD
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• The finite-temperature chiral transition in QCD with adjoint fermions
• Critical properties of a continuous family of XY noncollinear magnets
• Critical thermodynamics of three-dimensional chiral model for N > 3
• Bootstrapping MN and Tetragonal CFTs in Three Dimensions
• The normal-to-planar superfluid transition in Helium 3
• Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models
• Functional renormalization group approach to non-collinear magnets
• Chiral critical behavior in two dimensions from five-loop renormalization-group expansions
• Spin Stiffness of Stacked Triangular Antiferromagnets
• Multicritical behavior in frustrated spin systems with noncollinear order
• Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid
• Spin-density-wave order in cuprates
• Short-time dynamics of a family of XY noncollinear magnets
• Specific heat and muon spin resonance measurements in Gd(hfac)3NITiPr molecular magnetic chains: indications for a chiral phase without long range helical order
• Fixed points in frustrated magnets revisited
• Field-theory results for three-dimensional transitions with complex symmetries
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Simulating frustrated magnetism with spinor Bose gases
• Monte Carlo study of the critical properties of noncollinear Heisenberg magnets: $O(3)\times O(2)$ universality class
• Critical behavior of frustrated spin systems with nonplanar orderings
• First-order phase transitions in spinor Bose gases and frustrated magnets
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Critical Behavior of a General O(n)-symmetric Model of two n-Vector Fields in D=4-2 epsilon
• Frustrated magnets in three dimensions: a nonperturbative approach
• Frustrated Heisenberg Antiferromagnets between d=2 and d=3
• Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array