Chiral critical behavior of frustrated spin systems in two dimensions from five-loop renormalization-group expansions

@article{Calabrese2003ChiralCB,
  title={Chiral critical behavior of frustrated spin systems in two dimensions from five-loop renormalization-group expansions},
  author={Pasquale Calabrese and E. V. Orlov and Pietro Parruccini and A. I. Sokolov},
  journal={Physical Review B},
  year={2003},
  volume={67},
  pages={024413}
}
We analyze the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group (RG) approximation. The structure of the RG flow is studied for different N leading to the conclusion that the chiral fixed point governing the critical behavior of physical systems with N = 2 and N = 3 does not coincide with that given by the 1/N expansion. We show that the stable chiral fixed point for N≤N*, including N=2 and N=3, turns out to be a focus… 
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References

SHOWING 1-10 OF 36 REFERENCES
Chiral phase transitions: Focus driven critical behavior in systems with planar and vector ordering
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
Chiral Criticality near Two Dimensions
Critical behavior associated with the helical or noncollinear ordering for isotropic n >3-component spins is studied near d =2 dimensions based on an O ( n )× O (2) nonlinear σ model and the
Critical thermodynamics of two-dimensional systems in the five-loop renormalization-group approximation
The paper is devoted to the calculation of renormalization-group (RG) functions in the O(n)-symmetry two-dimensional model of the λϕ4 type in the five-loop approximation and to an analysis of the
Phase transitions in anisotropic superconducting and magnetic systems with vector order parameters: Three-loop renormalization-group analysis.
TLDR
The chiral fixed point of RG equations is found to exist and possess some domain of attraction provided N\ensuremath{\ge}4, and magnets with Heisenberg and XY-like spins should not demonstrate chiral critical behavior with unusual values of critical exponents; they can approach the chiral state only via first-order phase transitions.
Chiral exponents in frustrated spin models with noncollinear order
We compute the chiral critical exponents for the chiral transition in frustrated two- and three-component spin systems with noncollinear order, such as stacked triangular antiferromagnets (STA).
Critical behavior of frustrated spin models with noncollinear order
We study the critical behavior of frustrated spin models with noncollinear order, including stacked triangular antiferromagnets and helimagnets. For this purpose we compute the field-theoretic
Critical behavior of frustrated systems: Monte Carlo simulations versus renormalization group
We study the critical behavior of frustrated systems by means of the Padé-Borel resummed three-loop renormalization group expansions and numerical Monte Carlo simulations. Amazingly, for
Critical behavior of two-dimensional frustrated spin models with noncollinear order
We study the critical behavior of frustrated spin models with noncollinear order in two dimensions, including antiferromagnets on a triangular lattice and fully frustrated antiferromagnets. For this
Dynamic Approach to the Fully Frustrated XY Model
Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY model. By means of the short-time
...
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