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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| Published in: | Физика низких температур |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/118601 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862627342960033792 |
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| author | Merdan, Z. Güzelsoy, E. |
| author_facet | Merdan, Z. Güzelsoy, E. |
| 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. |
| collection | DSpace DC |
| container_title | 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.
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| first_indexed | 2025-12-07T13:38:22Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-118601 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T13:38:22Z |
| publishDate | 2011 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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| spelling | Merdan, Z. Güzelsoy, E. 2017-05-30T17:05:58Z 2017-05-30T17:05:58Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/118601 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Низкотемператуpный магнетизм Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton Article published earlier |
| spellingShingle | Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton Merdan, Z. Güzelsoy, E. Низкотемператуpный магнетизм |
| title | 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_short | 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 |
| topic | Низкотемператуpный магнетизм |
| topic_facet | Низкотемператуpный магнетизм |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118601 |
| work_keys_str_mv | AT merdanz finitesizescalingrelationsofthefourdimensionalisingmodelonthecreutzcellularautomaton AT guzelsoye finitesizescalingrelationsofthefourdimensionalisingmodelonthecreutzcellularautomaton |