Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton
The four-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ≤ L ≤ 8. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression...
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Назва видання: | Физика низких температур |
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/118601 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton / Z. Merdan, E. Güzelsoy // Физика низких температур. — 2011. — Т. 37, № 6. — С. 591–597. — Бібліогр.: 21 назв. — англ. |
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irk-123456789-1186012017-05-31T03:08:29Z Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton Merdan, Z. Güzelsoy, E. Низкотемператуpный магнетизм The four-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ≤ L ≤ 8. 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 for the 7, 14, and 21 independent simulations. The approximate values for the critical temperature of the infinite lattice, Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without logarithmic factor), 6.6921(22) (without logarithmic factor), 6.6909(2) (without logarithmic factor), 6.6822(13) (with logarithmic factor), 6.6819(11) (with logarithmic factor), 6.6808(8) (with logarithmic factor) are obtained from the intersection points of specific heat curves, the Binder parameter curves and the straight line fit of specific heat maxima for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results, 6.6802(1) and 6.6808(8), are in very good agreement with the series expansion results of Tc(∞) = 6.6817(15), 6.6802(2), the dynamic Monte Carlo result of Tc(∞) = 6.6803(1), the cluster Monte Carlo result of Tc(∞) = 6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm of Tc(∞) = 6.6802632 ± 5⋅10⁻⁵. The average values obtained for the critical exponent of the specific heat are calculated as α = –0.0402(15), –0.0393(12), –0.0391(11) for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained result, α = –0.0391(11), is agreement with the series expansions results of α = –0.12 ± 0.03 and the Monte Carlo using Metropolis and Wolff-cluster algorithm of α ≥ 0±0.04. However, α = –0.0391(11) isn’t consistent with the renormalization group prediction of α = 0. 2011 Article Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton / Z. Merdan, E. Güzelsoy // Физика низких температур. — 2011. — Т. 37, № 6. — С. 591–597. — Бібліогр.: 21 назв. — англ. 0132-6414 PACS: 05.45.–a, 75.10.Hk, 75.40.Cx http://dspace.nbuv.gov.ua/handle/123456789/118601 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Низкотемператуpный магнетизм Низкотемператуpный магнетизм |
| spellingShingle |
Низкотемператуpный магнетизм Низкотемператуpный магнетизм Merdan, Z. Güzelsoy, E. Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton Физика низких температур |
| description |
The four-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ≤ L ≤ 8. 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 for the 7, 14, and 21 independent simulations. The approximate values for the critical temperature of the infinite lattice, Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without logarithmic factor), 6.6921(22) (without logarithmic factor), 6.6909(2) (without logarithmic factor), 6.6822(13) (with logarithmic factor), 6.6819(11) (with logarithmic factor), 6.6808(8) (with logarithmic factor) are obtained from the intersection points of specific heat curves, the Binder parameter curves and the straight line fit of specific heat maxima for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results, 6.6802(1) and 6.6808(8), are in very good agreement with the series expansion results of Tc(∞) = 6.6817(15), 6.6802(2), the dynamic Monte Carlo result of Tc(∞) = 6.6803(1), the cluster Monte Carlo result of Tc(∞) = 6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm of Tc(∞) = 6.6802632 ± 5⋅10⁻⁵. The average values obtained for the critical exponent of the specific heat are calculated as α = –0.0402(15), –0.0393(12), –0.0391(11) for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained result, α = –0.0391(11), is agreement with the series expansions results of α = –0.12 ± 0.03 and the Monte Carlo using Metropolis and Wolff-cluster algorithm of α ≥ 0±0.04. However, α = –0.0391(11) isn’t consistent with the renormalization group prediction of α = 0. |
| format |
Article |
| author |
Merdan, Z. Güzelsoy, E. |
| author_facet |
Merdan, Z. Güzelsoy, E. |
| author_sort |
Merdan, Z. |
| title |
Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton |
| title_short |
Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton |
| title_full |
Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton |
| title_fullStr |
Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton |
| title_full_unstemmed |
Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton |
| title_sort |
finite-size scaling relations of the four-dimensional ising model on the creutz cellular automaton |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| topic_facet |
Низкотемператуpный магнетизм |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118601 |
| citation_txt |
Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton / Z. Merdan, E. Güzelsoy // Физика низких температур. — 2011. — Т. 37, № 6. — С. 591–597. — Бібліогр.: 21 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT merdanz finitesizescalingrelationsofthefourdimensionalisingmodelonthecreutzcellularautomaton AT guzelsoye finitesizescalingrelationsofthefourdimensionalisingmodelonthecreutzcellularautomaton |
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2023-10-18T20:32:36Z |
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2023-10-18T20:32:36Z |
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1796150474165977088 |