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Quantum Monte Carlo study of the transverse-field quantum Ising modelon infinite-dimensional structures
Umeå University, Faculty of Science and Technology, Department of Physics. (IceLab)
Korea Institute for Advanced Study, Seoul, Korea.
Department of Physics, Sungkyunkwan University, Suwon, Republic of Korea.
Department of Physics, Sungkyunkwan University, Suwon, Republic of Korea.
2011 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 84, 174419- p.Article in journal (Refereed) Published
Abstract [en]

In a number of classical statistical-physical models, there exists acharacteristic dimensionality called the upper critical dimension abovewhich one observes the mean-field critical behavior. Instead of constructinghigh-dimensional lattices, however, one can also considerinfinite-dimensional structures, and the question is whether this mean-fieldcharacter extends to quantum-mechanical cases as well. We thereforeinvestigate the transverse-field quantum Ising model on the globally couplednetwork and on the Watts-Strogatz small-world network by means of quantum MonteCarlo simulations and the finite-size scaling analysis. We confirm that bothof the structures exhibit critical behavior consistent with the mean-fielddescription. In particular, we show that the existing cumulant methodhas difficulty in estimating the correct dynamic critical exponent andsuggest that an order parameter based on the quantum-mechanicalexpectation value can be a practically useful numerical observable todetermine critical behavior when there is no well-defined dimensionality.

Place, publisher, year, edition, pages
American Physical Society , 2011. Vol. 84, 174419- p.
National Category
Condensed Matter Physics
URN: urn:nbn:se:umu:diva-50288DOI: 10.1103/PhysRevB.84.174419OAI: diva2:461356
Available from: 2011-12-05 Created: 2011-12-02 Last updated: 2011-12-13Bibliographically approved

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