Multi-grid Monte Carlo (II). Two-dimensional XY model

Robert G. Edwards; Jonathan Goodman; Alan D. Sokal

doi:10.1016/0550-3213(91)90357-4

Multi-grid Monte Carlo (II). Two-dimensional XY model

Robert G. Edwards, Jonathan Goodman, Alan D. Sokal

Mathematics

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

Abstract

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm applied to the two-dimensional XY model, on lattices up to 128 × 128. In the low-temperature (spin-wave) phase, we find that critical slowing-down is completely eliminated (z = 0). On the high-temperature side of critically, we find that the dynamic critical exponent is z = 1.4±0.3, compared to z = 2.1±0.3 for the heat-bath algorithm. We attribute the remaining critical slowing-down on the high-temperature side of criticality to the limited effectiveness of the MGMC updates in creating and destroying widely separated vortex-antivortex pairs.

Original language	English (US)
Pages (from-to)	289-327
Number of pages	39
Journal	Nuclear Physics, Section B
Volume	354
Issue number	2-3
DOIs	https://doi.org/10.1016/0550-3213(91)90357-4
State	Published - May 6 1991

ASJC Scopus subject areas

Nuclear and High Energy Physics

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@article{c036e7153f404358be6e0d3781e59342,

title = "Multi-grid Monte Carlo (II). Two-dimensional XY model",

abstract = "We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm applied to the two-dimensional XY model, on lattices up to 128 × 128. In the low-temperature (spin-wave) phase, we find that critical slowing-down is completely eliminated (z = 0). On the high-temperature side of critically, we find that the dynamic critical exponent is z = 1.4±0.3, compared to z = 2.1±0.3 for the heat-bath algorithm. We attribute the remaining critical slowing-down on the high-temperature side of criticality to the limited effectiveness of the MGMC updates in creating and destroying widely separated vortex-antivortex pairs.",

author = "Edwards, {Robert G.} and Jonathan Goodman and Sokal, {Alan D.}",

note = "Funding Information: The computations reported here were carried out primarily on the VAX 860() and 8650 and Elxsi 6400 at New York University . Some computations were performed on the Cyber 205 at the John Von Neumann Supercomputer Center (JVNC). This work was supported in part by the US National Science Foundation grants PHY-8413569, PHY-8715995, DMS-8705599 and DMS-8911273, by the US Department of Energy through contract DE-FC05-85ER250000, and by JVNC grant NAC-705. One of the authors (J.G.) was partially supported by a Sloan Foundation Fellowship and by DARPA.",

year = "1991",

month = may,

day = "6",

doi = "10.1016/0550-3213(91)90357-4",

language = "English (US)",

volume = "354",

pages = "289--327",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

number = "2-3",

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T1 - Multi-grid Monte Carlo (II). Two-dimensional XY model

AU - Edwards, Robert G.

AU - Goodman, Jonathan

AU - Sokal, Alan D.

N1 - Funding Information: The computations reported here were carried out primarily on the VAX 860() and 8650 and Elxsi 6400 at New York University . Some computations were performed on the Cyber 205 at the John Von Neumann Supercomputer Center (JVNC). This work was supported in part by the US National Science Foundation grants PHY-8413569, PHY-8715995, DMS-8705599 and DMS-8911273, by the US Department of Energy through contract DE-FC05-85ER250000, and by JVNC grant NAC-705. One of the authors (J.G.) was partially supported by a Sloan Foundation Fellowship and by DARPA.

PY - 1991/5/6

Y1 - 1991/5/6

N2 - We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm applied to the two-dimensional XY model, on lattices up to 128 × 128. In the low-temperature (spin-wave) phase, we find that critical slowing-down is completely eliminated (z = 0). On the high-temperature side of critically, we find that the dynamic critical exponent is z = 1.4±0.3, compared to z = 2.1±0.3 for the heat-bath algorithm. We attribute the remaining critical slowing-down on the high-temperature side of criticality to the limited effectiveness of the MGMC updates in creating and destroying widely separated vortex-antivortex pairs.

AB - We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm applied to the two-dimensional XY model, on lattices up to 128 × 128. In the low-temperature (spin-wave) phase, we find that critical slowing-down is completely eliminated (z = 0). On the high-temperature side of critically, we find that the dynamic critical exponent is z = 1.4±0.3, compared to z = 2.1±0.3 for the heat-bath algorithm. We attribute the remaining critical slowing-down on the high-temperature side of criticality to the limited effectiveness of the MGMC updates in creating and destroying widely separated vortex-antivortex pairs.

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