The Finite-Size Scaling Study of the Specific Heat and the Binder Parameter of the Two-Dimensional Ising Model for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

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dc.contributor.authorMerdan, Ziya
dc.contributor.authorBayırlı, Mehmet
dc.contributor.authorÖzturk, Mustafa Kemal
dc.date.accessioned2020-06-25T17:48:10Z
dc.date.available2020-06-25T17:48:10Z
dc.date.issued2009
dc.departmentKırıkkale Üniversitesi
dc.description.abstractThe two-dimensional Ising model with nearest-neighbour pair interactions is simulated oil the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 80, 120, 160, and 200. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T-c = 2.287(6) T-c = 2.269(3), and T-c =2.271(1) are obtained from the intersection points of specific heat curves. Binder parameter curves, and the straight line fit of specific heat maxima, respectively. These results are in agreement with the theoretical value (T-c =2.269) within the error limits. The values obtained for the critical exponent of the specific heat, alpha = 0.04(25) and alpha = 0.03(l), are in agreement with alpha = 0 predicted by the theory. The values for the Binder parameter by using the finite-size lattices with the linear dimension L = 80, 120, 160, and 200 at T-c = 2.269(3) are calculated as g(L)(T-c) = -1.833(5), g(L)(T-c) = -1.834(3), g(L)(T-c) = -1.832(2), and g(L)(T-c) = -1.833(2), respectively. The value of the infinite lattice for the Binder parameter, g(L)(T-c) = -1.834(11), is obtained from the straight line fit of g(L)(T-c) = -1.833(5), g(L)(T-c) = -1.834(3), g(L)(T-c) = -1.832(2), and g(L)(T-c) = -1.833(2) versus L = 80, 120, 160, and 200, respectively.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1515/zna-2009-1212
dc.identifier.endpage854en_US
dc.identifier.issn0932-0784
dc.identifier.issn1865-7109
dc.identifier.issue12en_US
dc.identifier.scopus2-s2.0-73049102646
dc.identifier.scopusqualityQ2
dc.identifier.startpage849en_US
dc.identifier.urihttps://doi.org/10.1515/zna-2009-1212
dc.identifier.urihttps://hdl.handle.net/20.500.12587/4338
dc.identifier.volume64en_US
dc.identifier.wosWOS:000274113600012
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWalter De Gruyter Gmbhen_US
dc.relation.ispartofZeitschrift Fur Naturforschung Section A-A Journal Of Physical Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectIsing Modelen_US
dc.subjectCellular Automatonen_US
dc.subjectFinite-Size Scalingen_US
dc.subjectScanning Methoden_US
dc.titleThe Finite-Size Scaling Study of the Specific Heat and the Binder Parameter of the Two-Dimensional Ising Model for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregationen_US
dc.typeArticle

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