Reflections in submanifolds

Tondeur, Philippe; Vanhecke, Lieven

doi:10.1007/bf00147801

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A3 Fixed Points Of Isometries1

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1989

1999

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Article5

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Cited by 6 publications

(1 citation statement)

References 14 publications

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“…1. Vanhecke and collaborators [86,87,88,89,90,91] have recently investigated reflections in Riemannian manifolds from a point of view opposite (but complementary) to ours. We start from an involutive isometry and seek to study its fixed-point manifold.…”

Section: A3 Fixed Points Of Isometriesmentioning

confidence: 89%

Wolff-type embedding algorithms for general nonlinear σ-models

et al. 1993

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We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on a Wolff-type embedding of Ising spins into the target manifold M . We argue heuristically that, at least for an asymptotically free model, such an algorithm can have dynamic critical exponent z ≪ 2 only if the embedding is based on an (involutive) isometry of M whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z int,M 2 = 1.5 ± 0.5 (subjective 68% confidence interval), in agreement with our heuristic argument.

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Section: A3 Fixed Points Of Isometriesmentioning

confidence: 89%