arXiv:0811.2683 · Nuclear Physics B

Universal properties of frustrated spin systems: 1/N -expansion and renormalization group approaches

A. N. Ignatenko, V. Yu. Irkhin, A. A. Katanin

Published Jan 9, 2009• 2 citations

arXiv HTML PDF

DOI: 10.1016/j.nuclphysb.2009.01.004

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arXiv:0811.2683 · Nuclear Physics B

Universal properties of frustrated spin systems: 1/N -expansion and renormalization group approaches

A. N. Ignatenko, V. Yu. Irkhin, A. A. Katanin

Published Jan 9, 2009• 2 citations

arXiv HTML PDF

DOI: 10.1016/j.nuclphysb.2009.01.004

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

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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. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.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. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.

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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. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.