Series expansion research of the phase transition for the spin statistical systems
| Project/Area Number |
12640382
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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 |
物性一般(含基礎論)
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| Research Institution | Osaka Prefectural College of Technololy |
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Principal Investigator |
ARISUE Hiroaki Osaka Prefectural College of Technololy, Professor, 教授 (10175987)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2003: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥2,500,000 (Direct Cost: ¥2,500,000)
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| Keywords | phase transition / Ising model / high-temperature expansion / finite lattice method / critical exponent / specific heat / magnetic susceptibility / correlation length / 自由エネルギー |
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| Research Abstract |
The finite lattice method is the most efficient method to generate the high-and low-temperature expansion series for the statistical system in two dimensions, but it had not been overwhelming the diagramatic method in three dimensions. In 2000 the head investigator H. Arisue and his collaborator T. Fujiwara (Professor of Kitasato University) developed a new algorithm of the finite lattice method, which enables us to generate the high-temperature series for the Ising model in three dimensions in much higher order than the previous finite lattice method and the diagramatic method. In fact we extended the high-temperature series for the specific heat of the Ising model in three dimensions from the previous 26th order to 46th order in the inverse temperature using the new algorithm in 2000 and 2001 and to 50th order in 2002. We also extended the high-temperature series for the magnetic susceptibility of the same model to 32nd order by the new algorithm from 25th order given by the diagramatic method. In 2003 we applied the algorithm to the high-temperature expansion of the second moment correlation length to 32nd order. These calculations were done partly by the workstation introduced in 2000 and partly by the calculation server at Yukawa Institute for Fundamental Physics, Kyoto University and the massively parallel supercomputer CP-PACS, Tuskuba University. The obtained series for the second moment correlation length were combined with the series for the magnetic susceptibility, giving gave the estimate of the phase transition point of the model in the accuracy of 7. digits, which coincides the estimate by the recent large-scaled numerical simulation, and also giving the estimate for the critical exponents of the magnetic susceptibility and the correlation length in the accuracy of 5 digits, which is the most precise when compared with the estimate by the various other methods.
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Report
(5 results)
Research Products
(13 results)
