Probabilistic investigation of phase transitions for lattice spin systems

晶格自旋系统相变的概率研究

• 批准号: 07640335
• 负责人: KURODA Koji
• 金额: $ 0.64万
• 依托单位: College of Humanities and Sciences, Nihon Univ.
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640335/
• 关键词: Gibbs state; Interface; Polymer expansion; Large deveation; Limit theorem; standard wall; Gibhs State; Large doviation; Limit theolem; Gibbs measure; Ising model; Interfce; algebraic formalism

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.

用一族基本形状“标准壁”来描述三维Ising模型的正负相界面，并给出了具有长程多体相互作用的标准壁系统的Gibbs态概率分布。研究了界面上随机场的一个极限定理和一个大偏差原理。特别地，我们考虑了标准壁w在[o，tL] * [o，sL]中的泛函F（w）的重新标度和以及由外部标准壁封闭的域的体积。为了研究极限定理和大偏差原理，必须得到标准壁的相关函数的性质，如聚类性质。我们通过使用一种簇展开的方法得到了这些相关函数的估计。该方法有望推广到更一般的格点系统。我们正试图把这种方法推广到更一般的情况。

项目成果

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K.Motegi：“Seifert 纤维歧管和 Dehn 手术”拓扑。

M.Suzuki: "Blow analytic moduli of analytic functions of two variables" Suurikan Kokyuroku "Singularity of differential map : Topology and its Application". 33-40 (1996)

M.Suzuki：“二变量解析函数的解析模”Suurikan Kokyuroku“微分映射的奇点：拓扑及其应用”。

A.Saito: "Two recursive theorems on n-extendibility" Discrete Math.162. 319-323 (1996)

A.Saito：“关于 n 可扩展性的两个递归定理”离散数学.162。

Koji Kuroda: "Clustering property of correlation functions for standard wall system" Proc. of Inst. of Nat. Scie., Nihon Univ.32. 77-98 (1997)

Koji Kuroda：“标准墙系统相关函数的聚类特性”Proc。

Seinosuke Toda: "On sets bounded Truth-table reducible to p-Selective sets" Informatique theorique et Applications/Theoretical Informatics and Appl.30.No2. 135-154 (1996)

Seinosuke Toda：“关于集合有界真值表可简化为 p-选择性集合”Informatique theorique et Applications/Theoretical Informatics 和 Appl.30.No2。