| Project/Area Number |
08640472
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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 | TOHOKU UNIVERSITY |
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Principal Investigator |
HORIGUCHI Tsuyoshi TOHOKU UNIVERSITY,GSIS,DEPT.OF COMPUTER AND MATH.SCIENCES,PROFESSOR, 大学院・情報科学研究科, 教授 (30005558)
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| Co-Investigator(Kenkyū-buntansha) |
HONDA Yasushi TOHOKU UNIVERSITY,GSIS,DEPT.OF COMPUTER AND MATH.SCIENCES,RESEARCH ASSOCIATE, 大学院・情報科学研究科, 助手 (20241531)
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| Project Period (FY) |
1996 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1997: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1996: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | layred magnet / XY model / KT transition / chirality transition / Monte Carlo simulations / finite size scaling / Ising model / frustration / 有限シズスケーリング |
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| Research Abstract |
In the research done in the fiscal year of 1996, we have found that there are two peaks in the specific heat for an XY model on a two-layr triangular lattice by Monte Carlo simulations (MCs). We have clarified that one of two peaks of the specific heat is due to a strange behavior of the chirality ; this is a new type of phase transition and occurs in some range of interaction parameters where there is a competition between the frustrated layr and the unfrustrated layr. In the research done in the fiscal year of 1997, we have investigated the critical phenomena for the new phase transition and found alpha=0.29 (9) and beta=0.253 (3) by means of finite size scaling analyzes ; alpha is the critical exponent for the specific heat and beta is the one for a steep change of the chirality (submitted to Physica A,1998). In order to investigate a universality of the new critical phenomena, we have investigated the XY model on a three-layr triangular lattice in which the first layr and the third
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layr have an antiferromagnetic interaction and the second layr has a ferromagnetic interaction. We have found the same type of phase transition in some range of interaction parameters and the nature of the critical phenomena is the same as that in the two-layr triangular lattice (preprint, 1998). We have also investigated the XY model on a four-layr triangular lattice. The results for four-layr triangular lattice will be presented in the 1998 spring-meeting of the Physical Society of Japan.
We have investigated the nature of phase transition for the Ising model on two-layr lattices, since the chirality has the same nature as the Ising spin in the low-temperature (Physica A,238 (1997) 295 ; JPSJ,66 (1997) 3053 ; JPSJ,67 (1998) to appear). In order to investigate the nature of the phase transition found in the present research proposal by a different approach from MCs, we have formulated the density matrix renormalization group method for the XY model (PRE,56 (1997) 3920). Its application to the two-layr XY model will be presented in the 1998 spring-meeting of the Physical Society of Japan. For an XY model on many-layr lattice, we have investigated the system reduced to a one-dimensional system of finite length (submitted to Physica A,1998). Less
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