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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146613 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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Sasakura, N. Sato, Y. 2019-02-10T10:03:09Z 2019-02-10T10:03:09Z 2014 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 https://nasplib.isofts.kiev.ua/handle/123456789/146613 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. We would like to thank Des Johnston for some communications. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exact Free Energies of Statistical Systems on Random Networks Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Exact Free Energies of Statistical Systems on Random Networks |
| spellingShingle |
Exact Free Energies of Statistical Systems on Random Networks Sasakura, N. Sato, Y. |
| 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 |
| author |
Sasakura, N. Sato, Y. |
| author_facet |
Sasakura, N. Sato, Y. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT sasakuran exactfreeenergiesofstatisticalsystemsonrandomnetworks AT satoy exactfreeenergiesofstatisticalsystemsonrandomnetworks |
| first_indexed |
2025-12-07T18:17:03Z |
| last_indexed |
2025-12-07T18:17:03Z |
| _version_ |
1850874447785885696 |