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STUDY ON CRITICAL PHENOMENA OF LAYERED XY MODEL WITH COMPETING INTERACTIONS BY MONTE CARLO SIMULATIONS

Research Project

Project/Area Number 08640472
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 物性一般(含基礎論)
Research InstitutionTOHOKU UNIVERSITY

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)

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)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
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)
Keywordslayred 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
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 … More 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

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 堀口 剛・津嶋 紀宏: "Shift exponent and breakdown of universality for the two-layer Ising model on a square lattice" Physics A. 238. 295-306 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 津嶋 紀宏・本田 泰・堀口 剛: "Critical properties of a spin-3/2 Ising model on a square lattice" J.Phys.Soc.Japan. 66. 3053-3062 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 津嶋 紀宏・堀口 剛: "Phase diagram of spin-3/2 Ising model on a square lattice in terms of corner transfer matrix renormalization group method" J.Phys.Soc.Japan. 67(印刷中). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 本田 泰・堀口 剛: "Density-matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model" Physical Review E. 56. 3920-3926 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Horiguchi and N.Tsushima: "Shift exponent and breakdown of universality for the two-layr Ising model on a square lattice" Physica A. 238. 295-306 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Tsushima and T.Horiguchi: "Critical properties of a spin-3/2 Ising model on a square lattice" J.Phys.Soc.Japan. 66. 3053-3062 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Tsushima, Y Honda and T.Horiguchi: "Phase diagram of spin-3/2 Ising modelon a square lattice in terms of corner transfer matrix renormalization group method" J.Phys.Soc.Japan. 67, (in printing). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Honda and T.Horiguchi: "Density-matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model" Physical Review E. 56. 3920-3926 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 堀口 剛・津嶋 紀宏: "Shift exponent and breakdown of universality for…" Physica A. 238. 295-306 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 津嶋 紀宏・本田 泰・堀口 剛: "Critical properties of a spin-3/2 Ising model on a…" J.Phys.Soc.Japan. 66. 3053-3062 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 津嶋 紀宏・堀口 剛: "Phase diagram of spin-3/2 Ising model on a square…" J.Phys.Soc.Japan. 67(掲載決定印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] 本田 泰・堀口 剛: "Density-matrix renormalization group for the…" Phys.Reu.E. 56. 3920-3926 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 本田泰・堀口剛: "Critical phase of magnetic hard hexagon model on a triangular lattice" Phys.Rev.E. 55・1. 194-198 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 堀口剛・津嶋紀宏: "shift exponent and breakdown of universality for the two-layer Ising model・・・" physica A. (掲載決定 印刷中). (1977)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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