Research of the Spin Statistical System by the High Order Calculation of the High and Low-Temperature Expansion Series
| Project/Area Number |
16540353
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical physics/Fundamental condensed matter physics
|
|---|
| Research Institution | Osaka Prefectural College of Technology |
|---|
Principal Investigator |
ARISUE Hiroaki Osaka Prefectural College of Technology, 総合工学システム学科, Professor (10175987)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ARISUE Hiroaki Osaka Prefectural College of Technology, Professor (10175987)
|
|---|
| Project Period (FY) |
2004 – 2007
|
| Project Status |
Completed (Fiscal Year 2007)
|
| Budget Amount *help |
¥4,050,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥2,100,000 (Direct Cost: ¥2,100,000)
|
|---|
| Keywords | phase transition / XY model / high-temperature expansion / finite lattice method / critical exponent / specific heat / magnetic susceptibility / correlation length |
|---|
| Research Abstract |
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.
|
Report
(5 results)
Research Products
(12 results)
