Phase transitions in the Potts model on complex networks
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the topology of a network. We consider the q-state Potts...
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| Дата: | 2013 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2013
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/120814 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Phase transitions in the Potts model on complex networks / M. Krasnytska, B. Berche, Yu. Holovatch// Condensed Matter Physics. — 2013. — Т. 16, № 2. — С. 2:1-15. — Бібліогр.: 54 назв. — англ. |
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irk-123456789-1208142017-06-14T03:02:40Z Phase transitions in the Potts model on complex networks Krasnytska, M. Berche, B. Holovatch, Yu. The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the topology of a network. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent \lambda. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known often to give asymptotically exact results. Depending on particular values of q and \lambda one observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find a correspondence between the magnetic exponents and those describing percolation on a scale-free network. Interestingly, logarithmic corrections to scaling appear at \lambda=4 in this case. Модель Поттса є однiєю з найпопулярнiших моделей статистичної фiзики. Бiльшiсть робiт, виконаних ранiше, стосувалась ґраткової версiї цiєї моделi. Однак багато природних та створених людиною систем набагато краще описуються топологiєю мережi. Ми розглядаємо q-станову модель Поттса на нескорельованiй безмасштабнiй мережi iз степенево згасною функцiєю розподiлу ступенiв вузлiв iз показником λ. Працюємо в наближеннi середнього поля, оскiльки для систем на нескорельованих безмасштабних мережах цей метод часто дозволяє отримати асимптотично точнi результати. В залежностi вiд значень q та λ, спостерiгаємо фазовi переходи першого чи другого роду, або ж система залишається впорядкованою при будь-якiй температурi. Також розглядаємо границю q = 1 (перколяцiя) та знаходимо вiдповiднiсть мiж магнiтними критичними показниками та показниками, що описують перколяцiю на безмаста-бнiй мережi. Цiкаво, що в цьому випадку логарифмiчнi поправки до скейлiнгу з’являються при λ = 4. 2013 Article Phase transitions in the Potts model on complex networks / M. Krasnytska, B. Berche, Yu. Holovatch// Condensed Matter Physics. — 2013. — Т. 16, № 2. — С. 2:1-15. — Бібліогр.: 54 назв. — англ. 1607-324X PACS: 64.60.ah, 64.60.aq, 64.60.Bd DOI:10.5488/CMP.16.23602 arXiv:1302.3386 http://dspace.nbuv.gov.ua/handle/123456789/120814 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the topology of a network. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent \lambda. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known often to give asymptotically exact results. Depending on particular values of q and \lambda one observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find a correspondence between the magnetic exponents and those describing percolation on a scale-free network. Interestingly, logarithmic corrections to scaling appear at \lambda=4 in this case. |
| format |
Article |
| author |
Krasnytska, M. Berche, B. Holovatch, Yu. |
| spellingShingle |
Krasnytska, M. Berche, B. Holovatch, Yu. Phase transitions in the Potts model on complex networks Condensed Matter Physics |
| author_facet |
Krasnytska, M. Berche, B. Holovatch, Yu. |
| author_sort |
Krasnytska, M. |
| title |
Phase transitions in the Potts model on complex networks |
| title_short |
Phase transitions in the Potts model on complex networks |
| title_full |
Phase transitions in the Potts model on complex networks |
| title_fullStr |
Phase transitions in the Potts model on complex networks |
| title_full_unstemmed |
Phase transitions in the Potts model on complex networks |
| title_sort |
phase transitions in the potts model on complex networks |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120814 |
| citation_txt |
Phase transitions in the Potts model on complex networks / M. Krasnytska, B. Berche, Yu. Holovatch// Condensed Matter Physics. — 2013. — Т. 16, № 2. — С. 2:1-15. — Бібліогр.: 54 назв. — англ. |
| series |
Condensed Matter Physics |
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AT krasnytskam phasetransitionsinthepottsmodeloncomplexnetworks AT bercheb phasetransitionsinthepottsmodeloncomplexnetworks AT holovatchyu phasetransitionsinthepottsmodeloncomplexnetworks |
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2023-10-18T20:38:02Z |
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2023-10-18T20:38:02Z |
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1796150716536979456 |