2017 Fiscal Year Final Research Report
multiple phase transition of probabilistic models on non-Euclidean graphs
| Project/Area Number |
15K17716
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Ibaraki University |
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Principal Investigator |
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| Research Collaborator |
Nemoto Koji 北海道大学, 大学院理学研究院, 教授
Nogawa Tomoaki 東邦大学, 医学部, 講師
Iwase Yuta 茨城大学, 大学院理工学研究科, 院生
Ukita Yuki 北海道大学, 大学院理学院, 院生
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 複雑ネットワーク / ネットワーク科学 / 格子確率モデル / パーコレーション / 感染症モデル / 相転移 / 臨界現象 |
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| Outline of Final Research Achievements |
It is known that mathematical models placed on non-Euclidean graphs, e.g. complex networks and nonamenable graphs, often exhibit novel phase transitions, which are never observed in Euclidean systems. In order to unveil the relationship between the structure of networks and phase transitions thereon, we investigated the following topics: (1) the statistical properties of the critical phase for bond percolation (in tree), (2) the origin of the absence of the ordered state for site percolation in hierarchical networks, (3) the characterization of the nonequilibrium multiple phase transitions for the contact process (in tree and Farey graph), and (4) the effect of the initial condition on the phase transitions of the infectious disease models in complex networks.
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| Free Research Field |
統計物理
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