Finite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatons

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dc.contributor.authorMerdan, Z.
dc.contributor.authorGuzelsoy, E.
dc.date.accessioned2020-06-25T17:51:46Z
dc.date.available2020-06-25T17:51:46Z
dc.date.issued2011
dc.departmentKırıkkale Üniversitesi
dc.description.abstractThe four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4 <= L <= 8. The temperature variations and finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for 7, 14, and 21 independent simulations. Approximate values for the critical temperature of the infinite lattice of T-c(infinity) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without the logarithmic factor), 6.6921(22) (without the logarithmic factor), 6.6909(2) (without the logarithmic factor), 6.6822(13) (with the logarithmic factor), 6.6819(11) (with the logarithmic factor), and 6.6808(8) (with the logarithmic factor) are obtained from the intersection points of the specific heat curves, the Binder parameter curves, and straight line fits of specific heat maxima for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the results, 6.6802(1) and 6.6808(8), are in very good agreement with the results of a series expansion of T-c(infinity), 6.6817(15) and 6.6802(2), the dynamic Monte Carlo value T-c(infinity) = 6.6803(1), the cluster Monte Carlo value T-c(infinity) = 6.680(1), and the Monte Carlo value using the Metropolis-Wolff cluster algorithm T-c(infinity) = 6.680263265+/-5 . 10(-5). The average values calculated for the critical exponent of the specific heat are a = -0.0402(15), -0.0393(12), -0.0391(11) with 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the result, alpha = -0.0391(11), agrees with the series expansions result, alpha = -0.12+/-0.03 and the Monte Carlo result using the Metropolis-Wolff cluster algorithm, a >= 0+/-0.04. However, alpha=-0.0391(11) is inconsistent with the renormalization group prediction of alpha=0. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3610180]en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1063/1.3610180
dc.identifier.endpage475en_US
dc.identifier.issn1063-777X
dc.identifier.issn1090-6517
dc.identifier.issue6en_US
dc.identifier.scopus2-s2.0-80051555481
dc.identifier.scopusqualityQ3
dc.identifier.startpage470en_US
dc.identifier.urihttps://doi.org/10.1063/1.3610180
dc.identifier.urihttps://hdl.handle.net/20.500.12587/4983
dc.identifier.volume37en_US
dc.identifier.wosWOS:000293794700004
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Physicsen_US
dc.relation.ispartofLow Temperature Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectcellular automataen_US
dc.subjectcritical exponentsen_US
dc.subjectIsing modelen_US
dc.subjectMonte Carlo methodsen_US
dc.subjectrenormalisationen_US
dc.subjectspecific heaten_US
dc.titleFinite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatonsen_US
dc.typeArticle

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