Research of the Spin Statistical System by the High Order Calculation of the High and Low-Temperature Expansion Series

高低温展开级数高阶计算的自旋统计系统研究

• 批准号: 16540353
• 负责人: ARISUE Hiroaki
• 金额: $ 2.59万
• 依托单位: Osaka Prefectural College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16540353/
• 关键词: phase transition; XY model; high-temperature expansion; finite lattice method; critical exponent; specific heat; magnetic susceptibility; correlation length

The finite lattice method is the most efficient tool to generate the high- and low-temperature expansion series for the statistical system in two dimensions. The head investigator H. Arisue extended the high-temperature series of the free energy for the XY model on the square lattice to 48th order from the previous 22nd order of the inverse temperature by applying an improved algorithm of the finite lattice method. The algorithm was originally developed by H. Arisue and his collaborator K. Tabata for Solid-on-Solid model in two dimensions. The long series obtained for the free energy allows us to conclude that the behavior of the free energy is consistent to high accuracy with what is expected when the phase transition of the model is of the Kosterlitz-Thouless type. H. Arisue also calculated the high-temperature series of the susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to 33rd order by applying the improved algorithm of the finite lattice method. The long series obtained allows us to estimate the critical point of the phase transition as β =1.1200 (1) which is consistent with the most precise value obtained previously by the Monte Carlo simulation.

有限点阵法是生成二维统计系统的高温和低温展开级数的最有效工具。首席研究员H. Arisue运用改进的有限点阵法算法，将XY模型在方点阵上的自由能高温级数由原来的逆温度22阶扩展到48阶。该算法最初是由H. Arisue和他的合作者K. Tabata为二维固体对固体模型开发的。自由能的长序列使我们能够得出结论，当模型的相变为Kosterlitz-Thouless型时，自由能的行为与预期的行为具有很高的准确性。H. Arisue还采用有限点阵法的改进算法，计算了XY模型在33阶方点阵上的磁化率和相关函数的二阶矩和四阶矩的高温级数。获得的长序列使我们能够估计相变的临界点为β =1.1200(1)，这与之前通过蒙特卡罗模拟获得的最精确值一致。

项目成果

2次元XY模型の高温展開の高次計算

二维XY模型高温演化的高阶计算

• 发表时间: 2004
• 作者: 市川 翼;佐々木 寿彦;筒井 泉;有末 宏明
• 通讯作者: 有末 宏明

High-Temperature Expansion of the Free Energy in 2D XY Model

二维 XY 模型中自由能的高温膨胀

• 发表时间: 2007
• 期刊: Progress of Theoretical Physics Vol.118
• 作者: Y.Toya;Y.Kino;Kudo;H. Arisue
• 通讯作者: H. Arisue

Higher orders of the high-temperature expansion for the Ising model in three dimensions

• DOI: 10.1016/s0920-5632(03)02709-9
• 发表时间: 2003-09
• 期刊: arXiv: High Energy Physics - Lattice
• 作者: H. Arisue;T. Fujiwara;K. Tabata

High-Temperature Expansion of the Free Energy in the Two-Dimensional XY Model

二维 XY 模型中自由能的高温膨胀

• 发表时间: 2007
• 期刊: Progress of Theoretical Physics 118
• 作者: T.Cheon;I.Tsutsui;H.Arisue
• 通讯作者: H.Arisue

2次元XY模型の帯磁率の高温展開

二维 XY 模型中磁化率的高温演化

• 发表时间: 2006
• 作者: T. Cheon;I. Tsutsui;T. Fulop;有末 宏明
• 通讯作者: 有末 宏明