Exact Free Energies of Statistical Systems on Random Networks
Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of vertices, and show that the free energies can be exactly ev...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146613 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Exact Free Energies of Statistical Systems on Random Networks / N. Sasakura, Y. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1466132019-02-11T01:23:27Z Exact Free Energies of Statistical Systems on Random Networks Sasakura, N. Sato, Y. Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of vertices, and show that the free energies can be exactly evaluated in the thermodynamic limit by the Laplace method, and that the exact expressions can in principle be obtained by solving polynomial equations for mean fields. As demonstrations, we apply our method to the ferromagnetic Ising models on random networks. The free energy of the ferromagnetic Ising model on random networks with trivalent vertices is shown to exactly reproduce that of the ferromagnetic Ising model on the Bethe lattice. We also consider the cases with heterogeneity with mixtures of orders of vertices, and derive the known formula of the Curie temperature. 2014 Article Exact Free Energies of Statistical Systems on Random Networks / N. Sasakura, Y. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05C82; 37A60; 46N55; 82B20; 81U15; 83C15 DOI:10.3842/SIGMA.2014.087 http://dspace.nbuv.gov.ua/handle/123456789/146613 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of vertices, and show that the free energies can be exactly evaluated in the thermodynamic limit by the Laplace method, and that the exact expressions can in principle be obtained by solving polynomial equations for mean fields. As demonstrations, we apply our method to the ferromagnetic Ising models on random networks. The free energy of the ferromagnetic Ising model on random networks with trivalent vertices is shown to exactly reproduce that of the ferromagnetic Ising model on the Bethe lattice. We also consider the cases with heterogeneity with mixtures of orders of vertices, and derive the known formula of the Curie temperature. |
| format |
Article |
| author |
Sasakura, N. Sato, Y. |
| spellingShingle |
Sasakura, N. Sato, Y. Exact Free Energies of Statistical Systems on Random Networks Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Sasakura, N. Sato, Y. |
| author_sort |
Sasakura, N. |
| title |
Exact Free Energies of Statistical Systems on Random Networks |
| title_short |
Exact Free Energies of Statistical Systems on Random Networks |
| title_full |
Exact Free Energies of Statistical Systems on Random Networks |
| title_fullStr |
Exact Free Energies of Statistical Systems on Random Networks |
| title_full_unstemmed |
Exact Free Energies of Statistical Systems on Random Networks |
| title_sort |
exact free energies of statistical systems on random networks |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146613 |
| citation_txt |
Exact Free Energies of Statistical Systems on Random Networks / N. Sasakura, Y. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 12 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT sasakuran exactfreeenergiesofstatisticalsystemsonrandomnetworks AT satoy exactfreeenergiesofstatisticalsystemsonrandomnetworks |
| first_indexed |
2025-07-11T00:19:45Z |
| last_indexed |
2025-07-11T00:19:45Z |
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1837307722426482688 |