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dc.contributor.authorXu, Naen_US
dc.contributor.authorCastelnovo, Claudioen_US
dc.contributor.authorMelko, Roger G.en_US
dc.contributor.authorChamon, Claudioen_US
dc.contributor.authorSandvik, Anders W.en_US
dc.date.accessioned2018-12-06T18:32:08Z
dc.date.available2018-12-06T18:32:08Z
dc.date.issued2018-01-29
dc.identifier.citationN Xu, C Castelnovo, RG Melko, C Chamon, AW Sandvik. 2018. "Dynamic scaling of topological ordering in classical systems." Physical Review B (Condensed Matter), Vol. 97, Iss. 2, 024432. https://doi.org/10.1103/PhysRevB.97.024432
dc.identifier.issn0163-1829
dc.identifier.urihttps://hdl.handle.net/2144/32894
dc.description.abstractWe analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional Z2 (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a nonlocal order parameter (defined using Wilson loops) and a dynamic exponent z=2.70±0.03, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature—the Ising chain, the two-dimensional Z2 gauge model, and a three-dimensional star model (another variant of the Z2 gauge model). In these systems the correlation length diverges exponentially, in a way that is nonsmooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.en_US
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofPhysical Review B (Condensed Matter)
dc.subjectScience & technologyen_US
dc.subjectTechnologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectMaterials scienceen_US
dc.subjectPhysics, applieden_US
dc.subjectPhysics, condensed matteren_US
dc.subjectPhysicsen_US
dc.subjectCondensed matteren_US
dc.titleDynamic scaling of topological ordering in classical systemsen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1103/PhysRevB.97.024432
pubs.elements-sourcemanual-entryen_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.orcid0000-0002-8275-2024 (Chamon, Claudio)
dc.identifier.orcid0000-0002-5638-4619 (Sandvik, Anders W)


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