| Project/Area Number |
23540136
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kobe University |
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Principal Investigator |
HIGUCHI Yasunari 神戸大学, 理学(系)研究科(研究院), 教授 (60112075)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKEI Masato 横浜国立大学, 大学院工学研究院, 准教授 (60460789)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 2次元 Ising model / パーコレーション / 相分離曲線 / スケーリング極限 / 臨界指数 / ２次元 Ising model / イジングモデル / スケーリング関係式 / 臨界点 / 相分離線 / 2次元Ising 模型 / 国際研究者交流（米国） |
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| Outline of Final Research Achievements |
For the two-dimensional Ising model, at high temperature there is a critical value of magnetic field at or near which percolation probability of + spins changes rapidly. Several observables converge to zero or diverge at this critical magnetic field. We showed that like in the independent case, among exponents of divergence or convergence to zero there are some equalities called scaling relations. For this, we extended the so called Russo formula, valid for independent percolation, to the Ising model. We obtained two opposite type inequlities instead of one equality.
Further, at high temperatures, we showed the existence of limiting distribution of infinite clusters conditioned that it exists at the critical value of external field. This distribution is called the incipient infinite cluster measure.
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