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dc.contributor.authorRubin, Shanon J.en_US
dc.contributor.authorXu, Naen_US
dc.contributor.authorSandvik, Anders W.en_US
dc.date.accessioned2018-12-06T19:28:33Z
dc.date.available2018-12-06T19:28:33Z
dc.date.issued2017-05-22
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000402019300003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationShanon J Rubin, Na Xu, Anders W Sandvik. 2017. "Dual time scales in simulated annealing of a two-dimensional Ising spin glass." Physical Review E, Volume 95, Issue 5, 052133. https://doi.org/10.1103/PhysRevE.95.052133
dc.identifier.issn2470-0045
dc.identifier.issn2470-0053
dc.identifier.urihttps://hdl.handle.net/2144/32900
dc.description.abstractWe apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T=0 of the two-dimensional Ising model with random J=±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ∼Lz, are z=8.28±0.03 for the relaxation of the order parameter and z=10.31±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T→0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent zeq(T), for which previous studies have found a divergent behavior: zeq(T→0)→∞. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.en_US
dc.description.sponsorshipWe thank Anatoli Polkovnikov, Claudio Chamon, and David Huse for stimulating discussions. The research was supported by the NSF under Grant No. DMR-1410126 and by Boston University's Undergraduate Research Opportunities Program. Computations were carried out on Boston University's Shared Computing Cluster. (DMR-1410126 - NSF; Boston University's Undergraduate Research Opportunities Program)en_US
dc.languageEnglish
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofPhysical Review E
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectPhysics, fluids & plasmasen_US
dc.subjectPhysics, Mathematicalen_US
dc.subjectPhysicsen_US
dc.subjectCondensed matter physicsen_US
dc.subjectQuantum physicsen_US
dc.titleDual time scales in simulated annealing of a two-dimensional Ising spin glassen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1103/PhysRevE.95.052133
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Physicsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-5638-4619 (Sandvik, Anders W)


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