Dynamic critical behaviour of Wolff's algorithm for RPN σ-models

Sergio Caracciolo; Robert G. Edwards; Andrea Pelissetto; Alan D. Sokal

doi:10.1016/0920-5632(92)90344-R

Dynamic critical behaviour of Wolff's algorithm for RP^N σ-models

Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

We study the performance of a Wolff-type embedding algorithm for RP^N σ-models. We find that the algorithm in which we update the embedded Ising model à la Swendsen-Wang has critical slowing-down as z_x ≈ 1. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain z_x ≈ 0. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour of the first algorithm is connected to the poor performance of the Swendsen-Wang algorithm in dealing with a frustrated Ising model.

Original language	English (US)
Pages (from-to)	595-597
Number of pages	3
Journal	Nuclear Physics B (Proceedings Supplements)
Volume	26
Issue number	C
DOIs	https://doi.org/10.1016/0920-5632(92)90344-R
State	Published - 1992

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Nuclear and High Energy Physics

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@article{90e3e6a160e4441ab6fe31d129a95dd1,

title = "Dynamic critical behaviour of Wolff's algorithm for RPN σ-models",

abstract = "We study the performance of a Wolff-type embedding algorithm for RPN σ-models. We find that the algorithm in which we update the embedded Ising model {\`a} la Swendsen-Wang has critical slowing-down as zx ≈ 1. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain zx ≈ 0. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour of the first algorithm is connected to the poor performance of the Swendsen-Wang algorithm in dealing with a frustrated Ising model.",

author = "Sergio Caracciolo and Edwards, {Robert G.} and Andrea Pelissetto and Sokal, {Alan D.}",

note = "Funding Information: Critical slowingdown is thus nearly eliminated! We conclude that the embedding encodes well the collective modes of the RP Ir model, and that the failure of the practical version must be ascribed to the Ising subroutine . We thank Paolo Pasini and Ulli Wolff for helpful discussions and for sending us their unpublished data. The computations reported here were performed at the Centro di Calcolo, SNS, Pisa . The authors' research was supported in part by INFN, DOE contracts DE-FC05-85ER250000 and DE-FG02-90ER40581, NSF grant DMS-8911273, and NATO CRG-910251 .",

year = "1992",

doi = "10.1016/0920-5632(92)90344-R",

language = "English (US)",

volume = "26",

pages = "595--597",

journal = "Nuclear Physics B (Proceedings Supplements)",

issn = "0920-5632",

publisher = "Elsevier",

number = "C",

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TY - JOUR

T1 - Dynamic critical behaviour of Wolff's algorithm for RPN σ-models

AU - Caracciolo, Sergio

AU - Edwards, Robert G.

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

N1 - Funding Information: Critical slowingdown is thus nearly eliminated! We conclude that the embedding encodes well the collective modes of the RP Ir model, and that the failure of the practical version must be ascribed to the Ising subroutine . We thank Paolo Pasini and Ulli Wolff for helpful discussions and for sending us their unpublished data. The computations reported here were performed at the Centro di Calcolo, SNS, Pisa . The authors' research was supported in part by INFN, DOE contracts DE-FC05-85ER250000 and DE-FG02-90ER40581, NSF grant DMS-8911273, and NATO CRG-910251 .

PY - 1992

Y1 - 1992

N2 - We study the performance of a Wolff-type embedding algorithm for RPN σ-models. We find that the algorithm in which we update the embedded Ising model à la Swendsen-Wang has critical slowing-down as zx ≈ 1. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain zx ≈ 0. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour of the first algorithm is connected to the poor performance of the Swendsen-Wang algorithm in dealing with a frustrated Ising model.

AB - We study the performance of a Wolff-type embedding algorithm for RPN σ-models. We find that the algorithm in which we update the embedded Ising model à la Swendsen-Wang has critical slowing-down as zx ≈ 1. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain zx ≈ 0. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour of the first algorithm is connected to the poor performance of the Swendsen-Wang algorithm in dealing with a frustrated Ising model.

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EP - 597

JO - Nuclear Physics B (Proceedings Supplements)

JF - Nuclear Physics B (Proceedings Supplements)

IS - C

ER -

Dynamic critical behaviour of Wolff's algorithm for RP^N σ-models

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