| Project/Area Number |
62540261
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Nagaoka University of Technology |
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Principal Investigator |
OGUCHI Takehiko Nagaoka Univ. of Technology, Department of Sciences and Mathematics, Professor., 工学部, 教授 (70016137)
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| Co-Investigator(Kenkyū-buntansha) |
KITATANI Hidetsugu Nagaoka Univ. of Technology, Department of Sciences and Mathematics, Research As, 工学部, 助手 (70186245)
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| Project Period (FY) |
1987 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1989: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1988: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1987: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Quantum spin systems / Heisenberg model / Resonating valence bond / Ising model / Transfer matrix method / Finite-size scaling / Triangular lattice / Coherent-anomaly method / Resonating valence bond / ±Jモデル / 臨界指数η / Dual変換 / 反強磁性Heisenbergモデル / 時間反転のパリティ / 反強磁性三角格子のIsingモデル / 第2隣接相互作用 / finite-Size scaling / Kosterlitz-Thouless型の相 / Coherent Anomaly Method / Trotteyの公式 / 摂動計算 / 時間反転 / パリティ / 相関関数 |
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| Research Abstract |
1) Two new methods have been proposed to caluculate physical quantities. In both methods, the systems divided into several subsystems, so that we can fairly decrease the storage of computer. Therefore, we can deal with large systems which are so large that direct diagonalization is not possible. The first method is the application of Trotter-formulae and the second one is that of the peiturbational method.
2) Several properties of eigenvalues and eigenfunctions for finite antiferromagnetic Heisenberg model have been rigorously proved. One of the results is that the parity of the ground state is even for N=4,8,12,...and odd for N=2,6,10...(N is the total number of spins).
3) The theory of the resonating valence bond(RVB) for the antiferromagnetic Heisenberg model of spin 1/2 proposed by Anderson is generalized. It has been shown that the ground state of the system is represented by singlet bonds which connect not only nearest but also distant spins.
4) The correlation functions, the value of eta of paramagnetic-spin glass phase transition have been calculated by using screw transfer matrix methods.
5) The coherent-anomaly method is applied to the spin 1/2 ferromagnetic Heisenberg model to estimate the critical exponents.
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