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Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions
KTH, School of Engineering Sciences (SCI), Theoretical Physics. Texas A&M University, USA.
2018 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 3, article id 032104Article in journal (Refereed) Published
Abstract [en]

The fractal dimension of domain walls produced by changing the boundary conditions from periodic to antiperiodic in one spatial direction is studied using both the strong-disorder renormalization group algorithm and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or fewer space dimensions, the fractal dimension is lower than the space dimension. This means that interfaces are not space filling, thus implying that replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space dimension in six dimensions, indicating that replica symmetry breaking occurs above six dimensions. In two space dimensions, the strong-disorder renormalization group results for the fractal dimension are in good agreement with essentially exact numerical results, but the small difference is significant. We discuss the origin of this close agreement. For the greedy algorithm there is analytical expectation that the fractal dimension is equal to the space dimension in six dimensions and our numerical results are consistent with this expectation.

Place, publisher, year, edition, pages
American Physical Society, 2018. Vol. 97, no 3, article id 032104
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-224678DOI: 10.1103/PhysRevE.97.032104ISI: 000426782000001Scopus ID: 2-s2.0-85044235700OAI: oai:DiVA.org:kth-224678DiVA, id: diva2:1193049
Funder
Swedish Research Council, 642-2013-7837Göran Gustafsson Foundation for Research in Natural Sciences and Medicine
Note

QC 20180326

Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2018-03-26Bibliographically approved

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