Updated on 2024/10/10

写真a

 
MINAMI, Kazuhiko
 
Organization
Graduate School of Mathematics Division of Mathematics Advanced Topology Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Associate professor
Contact information
メールアドレス
Homepage
http://www.math.nagoya-u.ac.jp/~minami/

Degree 1

  1. 博士(理学)

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Research Areas 2

  1. Others / Others  / Statistical Physics

  2. Others / Others  / Mathematical Physics/Fundamental Theory of Physical Properties

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Current Research Project and SDGs 1

  1. Study on solvable lattice models

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Professional Memberships 1

  1. 日本物理学会

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Papers 32

  1. The Exact Susceptibility of the Spin-S Transverse Ising Chain with Next-nearest-neighbor Interactions

    Minami, K

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   Vol. 92 ( 5 )   2023.5

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  2. Onsager algebra and algebraic generalization of Jordan-Wigner transformation

    Minami, K

    NUCLEAR PHYSICS B   Vol. 973   2021.12

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  3. Geometric criterion for solvability of lattice spin systems

    Ogura, M; Imamura, Y; Kameyama, N; Minami, K; Sato, M

    PHYSICAL REVIEW B   Vol. 102 ( 24 )   2020.12

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  4. Exact solution of a cluster model with next-nearest-neighbor interaction

    Yanagihara, Y; Minami, K

    PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS   Vol. 2020 ( 11 )   2020.11

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    Language：Japanese  

    DOI： 10.1093/ptep/ptaa146

    Web of Science

  5. Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations

    Minami Kazuhiko

    NUCLEAR PHYSICS B   Vol. 939   page： 465 - 484   2019.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.nuclphysb.2018.12.029

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  6. Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

    Minami Kazuhiko

    NUCLEAR PHYSICS B   Vol. 925   page： 144 - 160   2017.12

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.nuclphysb.2017.10.004

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  7. Solvable Hamiltonians and fermionization transformations obtained from operators satisfying specific commutation relations, Reviewed

    Kazuhiko Minami

    J. Phys. Soc. Jpn.   Vol. 85   page： 024003   2016.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  8. Equivalence between the two-dimensional Ising model and the quantum XY chain with randomness and with open boundary. Reviewed

    Kazuhiko Minami

    Europhys. Lett.   Vol. 108   page： 30001   2014.10

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  9. Exact transverse susceptibility of one-dimensional random bond Ising model with alternating spin. Reviewed

    Kazuhiko Minami

    J. Phys. A: Math. Theor.   Vol. 46   page： 505005   2013.11

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  10. Fractal structure of a solvable lattice model Reviewed

    Kazuhiko Minami

    Int. J. Pure and Applied Math.   Vol. 59   page： 243-255   2010

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  11. Spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model Reviewed

    Jozef Strecka, Lucia Canova and Kazuhiko Minami

    Phys.Rev.E   Vol. 79   page： 051103   2009

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    Language：English   Publishing type：Research paper (scientific journal)  

    The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.

  12. Weak universal critical behavior and quantum critical point of the exactly soluble spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg and quartic Ising interactions Reviewed

    Jozef Strecka, Lucia Canova and Kazuhiko Minami

    AIP Conf. Proc.   Vol. 1198   page： 156-165   2009

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    Language：English   Publishing type：Research paper (scientific journal)  

  13. *The free energies of six-vertex models and the n-equivalence relation Reviewed

    Kazuhiko Minami

    J.Math.Phys.   Vol. 49   page： 033514   2008

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    The free energies of six-vertex models on general domain D with various boundary conditions are investigated with the use of the n-equivalence relation which classifies the thermodynamic limit properties. It is derived that the free energy of the six-vertex model on the rectangle is unique in the limit in which both the height and the width goes to infinity. It is derived that the free energies of the model on D are classified through the densities of left/down arrows on the boundary. Specifically the free energy is identical to that obtained by Lieb and Sutherland with the cyclic boundary condition when the densities are both equal to 1/2. This fact explains several results already obtained through the transfer matrix calculations. The relation to the domino tiling (or dimer, or matching) problems is also noted.

  14. Thermodynamic properties of a tetramer Ising-Heisenberg bond alternating chain as a model system for Cu(3-Chloropyridine)2(N3)2 (共著) Reviewed

    Phys.Rev. B   Vol. 72   page： 024459 (1-11)   2005

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    Language：English   Publishing type：Research paper (scientific journal)  

  15. An equivalence relation of boundary/initial conditions and the infinite limit properties Reviewed

    J.Phys.Soc.Jpn.   Vol. 74   page： 1640   2005

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  16. On the saturation field of magnets Reviewed

    J.Mag.Mag.Mat.   Vol. 270   page： 104   2004

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  17. Magnetic properties of a tetramer ferro-ferro-antiferro-antiferromagnetic Ising-Heisenberg bond alternating chain as a model systemfor Cu(3-Clpy)2(N3)2 (共著) Reviewed

    Czech.J.Phys.   Vol. 54 ( Suppl 4 ) page： 583   2004

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  18. Magnetization process of an S=1/2 tetramer chain withferromagnetic-ferrimagnetic-antiferromagnetic bond alternating interactions (共著) Reviewed

    J.Phys.Soc.Jpn.   Vol. 72   page： 943   2003

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  19. Thermodynamic properties of a quantum ferrimagnet formed byan S=1/2 tetramer chain (共著) Reviewed

    Prog.Theor.Phys.   Vol. 145   page： 150   2002

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    Language：English   Publishing type：Research paper (scientific journal)  

  20. High-field magnetization of an s=1/2 F-F-AF-AF tetramer chain (共著) Reviewed

    Physica B   Vol. 294-295   page： 30   2001

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    Language：English   Publishing type：Research paper (scientific journal)  

  21. Magnetization process of the S=1/2 and 1 ferrimagnetic chain and dimer (共著) Reviewed

    J.Phys.Soc.Jpn.   Vol. 68   page： 2214   1999

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    Language：English   Publishing type：Research paper (scientific journal)  

  22. Experimental and theoretical approach to finite-size effects in an S=1/2 antifervromagnetic Heisenberg open chain(共著) Reviewed

    Phys.Rev. B   Vol. 57   page： 8285   1998

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    Language：English   Publishing type：Research paper (scientific journal)  

  23. *The susceptibility in Arbitrary directions and the specific heat of general Ising-type chains with uniform, periodic and random structures Reviewed

    J.Phys.Soc.Jpn.   Vol. 67   page： 2255   1998

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  24. Magnetic properties of a quantum fervimagnet NiCu(pba)(H2O)32D2O(共著) Reviewed

    J.Phys.Soc.Jpn.   Vol. 67   page： 2209   1998

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    Language：English   Publishing type：Research paper (scientific journal)  

  25. The zero-field susceptibility of the transverse Ising chain with arbitrary spin Reviewed

    J.Phys. A   Vol. 29   page： 6395   1996

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  26. Mognetic susceptibility of the S=3/2 finite linear-chain Heisenberg antiferromagnet CsV1-χMgχCl3(共著) Reviewed

    J.Phys.(Cond. Mat.)   Vol. 8   page： 8407   1996

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    Language：English   Publishing type：Research paper (scientific journal)  

  27. *Non-universal critical behaviour of two-dimensional Ising systems (共著) Reviewed

    J.Phys. A   Vol. 27   page： 7301   1994

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  28. Non-universal critical behaviour of the two-dimensional Ising model with crossing bonds (共著) Reviewed

    Physica A   Vol. 192   page： 2152   1993

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  29. A two-dimensional Ising model with non-universal critical behaviour (共著) Reviewed

    Physica A   Vol. 195   page： 4457   1993

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  30. Non-universal critical behaviour of two-dimensional Ising models via two-body interactions (共著) Reviewed

    Phys. Lett. A   Vol. 180   page： 2179   1993

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  31. Coherent-anomaly method applied to the eight-vertex model (共著) Reviewed

    Physica A   Vol. 187   page： 2282   1992

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  32. Multi-effective-field theory -applications to the CAM analysis of the two-dimensional Ising model- (共著) Reviewed

    Physica A   Vol. 174   page： 3479   1991

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Books 4

  1. Lectures on Linear Algebra

    （ Role： Sole author）

    2020.1 

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    Language：Japanese

  2. 格子模型の数理物理

    南　和彦（ Role： Sole author）

    サイエンス社  2014.6 

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    Total pages：155   Language：Japanese Book type：Scholarly book

  3. Lectures on Calculus

    （ Role： Sole author）

    2010.1 

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    Language：Japanese

  4. Coherent-Anomary Method-Mean Field, Fluctuations and Systematics(共著)

    World Scietntific  1995 

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    Language：English

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KAKENHI (Grants-in-Aid for Scientific Research) 2

  1. 新しい対角化の手法による量子系の厳密解の研究

    Grant number：19K03668  2019.4 - 2024.3

    科学研究費助成事業  基盤研究(C)

    南 和彦

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    Authorship：Principal investigator 

    Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）

    新しく見出された対角化の方法による、2次元量子スピン系の厳密解の研究である。ハミルトニアンの各項が条件をみたすとき、交換関係と周期のみから自由エネルギーが厳密に導かれることを、申請者が見出した。条件をみたす演算子列から解ける模型が得られ、解くための変換も同時に自動的に得られる。既知の主要な模型の多くが、この方法で同じ手順で対角化できている。この手法を基礎に以下のテーマを扱う：
    1) Kitaev模型を特殊な場合として含む2次元系の可解模型の系列
    2) この手法による新しい2次元量子系の厳密解
    3) 手法自体の拡張による可解模型の新しいクラス
    4) 等価性、CFT、量子計算に関連する磁性物質等への応用
    本研究課題で扱われている手法で対角化される一連の模型の特別な場合であるtransverse Ising模型は、Ising相互作用にtranverse磁場をかけた単純であるが基本的な量子スピン模型である。Ising相互作用とtranverse磁場との非可換性から量子効果が現れる。1次元でスピン1/2の場合については、厳密解が得られる以前にFisherが零磁場のtransverse帯磁率を求め、その後、KatsuraそしてPfeutyが自由エネルギーを求めた。スピン1/2の場合の1次元transverse Ising模型はfree fermionに帰着されて解ける模型で、またスピン1/2の場合については、1次元transverse Ising模型と2次元正方格子Ising模型とが等価であることが分かっている。
    <BR>
    この模型について、一般のスピンSでは厳密解はまだ得られていないものの、零磁場の帯磁率および周期的なあるいはランダムな相互作用を持つ場合の帯磁率が導かれている（Minami, 1996年, 1998年, 2013年）。これらはいずれも最近接の相互作用のみを持つ模型である。
    <BR>
    この模型の次近接相互作用のある場合について、一般のスピンSでの零磁場のtransverse帯磁率を厳密に導出した。帯磁率の導出の鍵になるのは伝送行列であるが、次近接相互作用を伝送行列で扱うことができたためにこの導出が可能になった。帯磁率は低温の極限でSに依存せず、相互作用が特定の値をとるとき、温度T→0の極限で1/Tの発散を示す。
    transverse Ising模型の一般のスピンSでの帯磁率については、1996年、1998年、2013年の論文で扱ってきたが、伝送行列の特性からその議論は相互作用が最近接の場合に限られると考えていた。今回、1965年のOguchiのアイデアを利用してその議論を拡張し、次近接相互作用を持つ場合の帯磁率を厳密に導出することが出来た。次近接相互作用を含んでも低温での普遍性はそのまま成り立ち、基底状態が転移を示す点ではT→0で帯磁率は発散を示す。この発散は、転移点で基底状態が極めて高い縮退を示し、その結果として基底状態の状態空間の中でのキューリー則が成立したものとして理解できる。
    <BR>
    大阪大の磁性実験の研究者と議論したが、次近接相互作用のあるIsing鎖としては磁性物質としてはCsCoCl3などがあり、帯磁率の測定も可能であるようだ。
    free fermionの構造を持つ可解模型は重要な模型を多く含み、その周辺に同じ構造を持ついくつもの系列が見られる。一方でスピンSのtransverse Ising模型はその自由エネルギーはまだ得られておらず、またfree fermionの構造を持つとは考え難い。今回の結果をひとつの手がかりとして、可解模型の系列のfree fermionからの拡張を試みる。

  2. 格子模型のフラクタル構造と平衡および非平衡系への展開

    2007

    科学研究費補助金  基盤研究（Ｃ）（一般），課題番号：19540400

    南　和彦

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    Authorship：Principal investigator 

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Teaching Experience (On-campus) 2

  1. Calculus I

    2011

  2. Calculus II

    2011

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