1996 Fiscal Year Final Research Report Summary
Probabilistic investigation of phase transitions for lattice spin systems
| Project/Area Number |
07640335
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 | College of Humanities and Sciences, Nihon Univ. |
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Principal Investigator |
KURODA Koji College of Humanities and Sciences, Nihon Univ., Associate Prof., 文理学部, 助教授 (50153416)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAURA Yoshihiko College of Humanities and Sciences, Nihon Univ., Associate Prof., 文理学部, 専任講師 (90255597)
TODA Seinosuke College of Humanities and Sciences, Nihon Univ., Associate Prof., 文理学部, 助教授 (90172163)
MOTEGI Kimihiko College of Humanities and Sciences, Nihon Univ., Associate Prof., 文理学部, 助教授 (40219978)
SUZUKI Masahiko College of Humanities and Sciences, Nihon Univ., Associate Prof., 文理学部, 助教授 (00171249)
SAITO Akira College of Humanities and Sciences, Nihon Univ., Associate Prof., 文理学部, 助教授 (90186924)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Gibbs state / Interface / Polymer expansion / Large deveation / Limit theorem / standard wall |
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| Research Abstract |
An interface of plus minus phases for three dimensional Ising model is described by a family of elementary shapes called "standard walls", and its probability distribution is given as a Gibbs state for standard wall system with long range, multibody interaction. We investigated a limit theorem and a large deviation principle for random field on the interface. In particular we considered a rescaled sum of functionals F (w) for standard walls w in [o, tL] * [o, sL] and a volume of enclosed domain by outer standard walls. To investigate a limit theovem and a large deviation principle it was neccesary to obtain properties of correlation functions for standard walls such as clustering properties. We obtained these estimates for correlation functions by using a method of cluster expansion. This method is expected to extend to more general lattice system. We are trying to extend this method to more general cases.
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