Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension

Physical Review Letters
Zheng ZhuHelmut G Katzgraber

Abstract

Spin systems with frustration and disorder are notoriously difficult to study, both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated dynamics methods remain elusive for generic spin-glass-like systems. Here, we present a cluster algorithm for Ising spin glasses that works in any space dimension and speeds up thermalization by at least one order of magnitude at temperatures where thermalization is typically difficult. Our isoenergetic cluster moves are based on the Houdayer cluster algorithm for two-dimensional spin glasses and lead to a speedup over conventional state-of-the-art methods that increases with the system size. We illustrate the benefits of the isoenergetic cluster moves in two and three space dimensions, as well as the nonplanar chimera topology found in the D-Wave Inc. quantum annealing machine.

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Citations

Mar 5, 2016·Scientific Reports·Nicholas ChancellorPaul A Warburton
Apr 3, 2020·Reports on Progress in Physics·Philipp HaukeWilliam D Oliver
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wenlong WangHelmut G Katzgraber
May 22, 2019·Physical Review. E·Andrew J OchoaHelmut G Katzgraber
Dec 25, 2019·Physical Review. E·Forrest SheldonMassimiliano Di Ventra
Mar 15, 2020·Physical Review. E·Dilina PereraHelmut G Katzgraber
Apr 30, 2017·Physical Review Letters·M Baity-JesiUNKNOWN Janus Collaboration
May 16, 2018·Physical Review. E·Firas HamzeHelmut G Katzgraber
Jul 25, 2019·Physical Review. E·Zheng ZhuHelmut G Katzgraber
Sep 28, 2017·Physical Review. E·Wenlong WangHelmut G Katzgraber
Sep 11, 2019·Physical Review. E·Takuya OkuyamaMasanao Yamaoka
Aug 17, 2020·Physical Review. E·Hauke FajenA P Young

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