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Critical Behaviour of the Ising S=l/2 and S=l Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices

Published online by Cambridge University Press:  20 August 2015

F. W. S. Lima ,
J. Mostowicz  and
K. Malarz
F. W. S. Lima*
Affiliation:
Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550 Teresina, Piauí, Brazil
J. Mostowicz*
Affiliation:
Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
K. Malarz*
Affiliation:
Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
*
Corresponding author.Email:fwslima@gmail.com
Email:mostowicz@gmail.com
Email:malarz@agh.edu.pl
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Abstract

We investigate the critical properties of the Ising S = 1/2 and S = 1 model on (3,4,6,4) and (34,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, and ν basing on finite size scaling analysis. The calculated values of the critical temperature for S = 1 are kBTC/J=1.590(3), and kBTC/J=2.100(4) for (3,4,6,4) and (34,6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν, and 1/ν, for S=1 are β/ν=0.180(20), γ/ν=1.46(8), and 1/ν=0.83(5), for (3,4,6,4) and 0.103(8), 1.44(8), and 0.94(5), for (34,6) Archimedean lattices. Obtained results differ from the Ising S = 1/2 model on (3,4,6,4), (34,6) and square lattice. The evaluated effective dimensionality of the system for S = 1 are Deff=1.82(4), for (3,4,6,4), and Deff = 1.64(5) for (34,6).

Keywords

05.70.Ln05.50.+q75.40.Mg02.70.LqMonte Carlo simulationIsing modelcritical exponents
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 912 - 919
Copyright
Copyright © Global Science Press Limited 2011

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