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Volume 10, Issue 4
Critical Behaviour of the Ising S=1/2 and S=1 Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices

F. W. S. Lima, J. Mostowicz & K. Malarz

DOI: 10.4208/cicp.090910.021210a

Commun. Comput. Phys., 10 (2011), pp. 912-919.

Published online: 2011-10

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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).

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@Article{CiCP-10-912, author = {}, title = {Critical Behaviour of the Ising S=1/2 and S=1 Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {4}, pages = {912--919}, 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).

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.090910.021210a}, url = {http://global-sci.org/intro/article_detail/cicp/7468.html} }
TY - JOUR T1 - Critical Behaviour of the Ising S=1/2 and S=1 Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices JO - Communications in Computational Physics VL - 4 SP - 912 EP - 919 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.090910.021210a UR - https://global-sci.org/intro/article_detail/cicp/7468.html KW - AB -

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).

F. W. S. Lima, J. Mostowicz & K. Malarz. (2020). Critical Behaviour of the Ising S=1/2 and S=1 Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices. Communications in Computational Physics. 10 (4). 912-919. doi:10.4208/cicp.090910.021210a
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