Research on the formation and fluctuation of random shapes in mathematical models of statistical mechanics

统计力学数学模型中随机形状的形成与涨落研究

• 批准号: 12440027
• 负责人: HIGUCHI Yasunari
• 金额: $ 6.46万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440027/
• 关键词: Widom-Rowlinson model; phase separation; central limit theorem; local limit theorem; Wulff shape; phase structure; translation invariance; Gibbs states; 2次元Widom-Rowlinsonモデル; 相境界; 局所型極限定理; 表面張力; パーコレーション; 3粒子モデル; 2次元Ising model; 臨界温度; per

1. We found a new proof of the fact that there are only two extremal Gibbs states for the two dimensional Ising model based on the percolation argument. As an application of this new method, we proved that there are only two extremal points of translationally invariant Gibbs states for the two dimensional Widom-Rowlinson model for sufficiently low temperatures.2. We gave an estimate of the speed of convergence for the time constant of the first passage Ising percolation for temperatures above the critical point.3. We proved a Dobrushin-Hryniv type limit theorem for the two-dimensional Widom-Rowlinson model. The conditions for the result to hold are a little relaxed.

1. 我们发现了二维Ising模型只有两个极值Gibbs态的新证明。作为该方法的一个应用，我们证明了在足够低的温度下二维Widom-Rowlinson模型的平移不变Gibbs态只有两个极值点。我们给出了温度高于临界点时第一个通道的时间常数的收敛速度的估计。证明了二维Widom-Rowlinson模型的Dobrushin-Hryniv型极限定理。维持结果的条件有点宽松。

项目成果

Y. Nakanishi, Y. Ohyama: "Knots with given finite typeinvariatns and C_k-distance"J. Knot Theory and Its Ramifications. 10-7. 1041-1046 (2001)

Y. Nakanishi，Y. Ohyama：“具有给定有限类型不变性和 C_k 距离的结”J。

Y.Higuchi, Yu Zhang: "On the speed of convergence for two dimensional first-passage percolation"The Annals of Probability. 28. 353-378 (2000)

Y.Higuchi、张宇：“论二维第一通道渗滤的收敛速度”《概率年鉴》。

K.Fukuyama: "On the asymptotic distribution of pseudorandom functions"Monte Carlo Methods and Applications. 6. 167-174 (2000)

K.Fukuyama：“论伪随机函数的渐近分布”蒙特卡罗方法及其应用。

Y.Higuchi: "On the speed of convergence for two-dimensionsl first passage Ising percolation"The Annals of Probability. 28. 353-378 (2000)

Y.Higuchi：“关于二维第一通道伊辛渗透的收敛速度”《概率年鉴》。

K. Fukuyama: "An asymptotic property of gap series"Acta Mathematica Hungarica. 97. 209-216 (2002)

K. Fukuyama：“间隙级数的渐近性质”匈牙利数学报。