Fixed points in frustrated magnets revisited

Abstract

We analyze the validity of perturbative renormalization group estimates obtained within the fixed dimension approach of frustrated magnets. We reconsider the resummed five-loop beta-functions obtained within the minimal subtraction scheme without epsilon-expansion for both frustrated magnets and the well-controlled ferromagnetic systems with a cubic anisotropy. Analyzing the convergence properties of the critical exponents in these two cases we find that the fixed point supposed to control the second order phase transition of frustrated magnets is very likely an unphysical one. This is supported by its non-Gaussian character at the upper critical dimension d=4. Our work confirms the weak first order nature of the phase transition occuring at three dimensions and provides elements towards a unified picture of all existing theoretical approaches to frustrated magnets.

18 pages, 8 figures. This article is an extended version of arXiv:cond-mat/0609285

References in corpus (23)

• Nonperturbative renormalization group approach to frustrated magnets
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Heisenberg frustrated magnets: a nonperturbative approach
• Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$
• The critical behavior of frustrated spin models with noncollinear order
• Critical behavior of O(2)xO(N) symmetric models
• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• Chiral transitions in three-dimensional magnets and higher order ε-expansion
• Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering
• Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model
• Divergent Perturbation Series
• Randomly dilute Ising model: A nonperturbative approach
• Five-loop epsilon expansion for O(n)xO(m) spin models
• Summability of the perturbative expansion for a zero-dimensional disordered spin model
• On the criticality of frustrated spin systems with noncollinear order
• The finite-temperature chiral transition in QCD with adjoint fermions
• Critical thermodynamics of three-dimensional chiral model for N > 3
• Critical properties of a continuous family of XY noncollinear magnets
• Randomly dilute spin models with cubic symmetry
• New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop εexpansions
• First order phase transition in the frustrated triangular antiferromagnet CsNiCl3
• Short-time dynamics of a family of XY noncollinear magnets
• Universality classes of three-dimensional $mn$-vector model

Cited by in corpus (13)

• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Functional renormalization group approach to non-collinear magnets
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation
• Crossover Behavior from Decoupled Criticality
• 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
• Variety of Scaling Laws for DNA Thermal Denaturation
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Critical Exponents of the O(N)-symmetric ${\varphi }^4$ Model from the \boldmath{\large{ ${\epsilon }^7$}} Hypergeometric-Meijer Resummation
• Emergence of the 3D diluted Ising model universality class in a mixture of two magnets
• Phase diagram of Model C in the parametric space of order parameter and space dimensions