Kazuhiko MINAMI, bibliography
List of Publications
Kazuhiko Minami, Yoshihiko Nonomura, Makoto Katori and Masuo Suzuki:
Multieffectivefield theory: applications to the CAM analysis of the twodimensional Ising model
Physica A174 (1991) 479503
Kazuhiko Minami and Masuo Suzuki:
Coherentanomaly method applied to the eightvertex model
Physica A187 (1992) 282307
Kazuhiko Minami and Masuo Suzuki:
Nonuniversal critical behaviour of the twodimensional Ising model
with crossing bonds
Physica A192 (1993) 152166
Kazuhiko Minami and Masuo Suzuki:
A twodimensional Ising model with nonuniversal critical behaviour
Physica A195 (1993) 457473
Kazuhiko Minami and Masuo Suzuki:
Nonuniversal critical behaviour of twodimensional Ising models
via twobody interactions
Phys. Lett. A180 (1993) 179182

Abstract: The squarelattice Ising model with antiferromagnetic
nextnearestneighbour interaction and the Ising models
with the fourbody interaction are investigated.
The critical temperatures and the exponent gamma are estimated
with errors smaller than ~0.1% and ~1%, respectively.
The exponent gamma varies continuously.
The perturbation in terms of the interaction energy is also performed.
A sufficient condition for the relevant models
to have continuously varying critical exponents is found.
Kazuhiko Minami and Masuo Suzuki:
Nonuniversal critical behaviour of twodimensional Ising systems
J. Phys. A: Math. Gen. 27 (1994) 73017311
,
condmat/0404572

Abstract:
Two conditions are derived for Ising models
to show nonuniversal critical behaviour,
namely conditions concerning
1) logarithmic singularity of the specific heat and
2) degeneracy of the ground state.
These conditions are satisfied with the eightvertex model,
the AshkinTeller model, some Ising models with short or longrange interactions
and even Ising systems without the translational or the rotational invariance.
Masuo Suzuki, Kazuhiko Minami and Yoshihiko Nonomura:
Coherentanomaly method  recent development
Physica A205 (1994) 80100, proceedings
Masuo Suzuki, Xiao Hu, Makoto Katori, Adam Lipowski, Naomichi Hatano, Kazuhiko Minami and Yoshihiko Nonomura:
CoherentAnomaly Method  Mean Field, Fluctuations and Systematics
ed. by Masuo Suzuki, World Scientific, 1995
Hideki Yamazaki, Kazuhiko Minami and Kouichi Katsumata:
Magnetic susceptibility of the s=3/2 finite linearchain Heisenberg
antiferromagnet CsV1xMgxCl3
J. Phys. Cond.Mat. 8 (1996) 84078412
Kazuhiko Minami:
The zerofield susceptibility of the transverse Ising chain with arbitrary spin
J. Phys. A: Math. Gen. 29 (1996) 63956405

Abstract:
The zerofield susceptibility of the transverse
Ising chain with arbitrary spinS
is expressed in terms of the eigenvector
for the maximum eigenvalue of its transfer matrix.
As a result, the exact susceptibility is explicitly obtained
for S=1/2, 1, 3/2 and can be obtained at least for S smaller than or equal to 7/2.
The numerical calculations of the susceptibility for arbitrary spin are possible
and those for S=6, 12 and 24 are given.
It is also derived that the zerotemperature limit of the susceptibility
is independent of spinS.
Hitoshi Asakawa, Masaaki Matsuda, Kazuhiko Minami, Hideki Yamazaki
and Kouichi Katsumata:
Experimental and theoretical approach to finitesize effects
in an S=1/2 antiferromagnetic Heizenberg open chain
Phys.Rev.B57 (1998) 82858289
Masayuki Hagiwara, Kazuhiko Minami, Yasuo Narumi, Keiji Tatani
and Koichi Kindo:
Magnetic properties of a quantum ferrimagnet: NiCu(pba)(H2O)3 2D2O
J.Phys.Soc.Jpn.67 (1998) 22092211, condmat/9807348
Kazuhiko Minami:
The susceptibility in arbitrary directions and the specific heat
of general Isingtype chains with uniform, periodic and random structures
J.Phys.Soc.Jpn. 67 (1998) 22552269

Abstract:
The susceptibility in arbitrary directions, the
specific heat, the energy and the magnetization of general Isingtype chains
are exactly expressed in terms of the eigenvectors of
the transfer matrix corresponding to the Isingtype interaction.
These quantities, as a result, can be explicitly obtained for
small spin values and generally obtained from the solution of corresponding
eigenvalue problem of finite degree. Numerical estimations are
easy for arbitrary spin values. This formula includes the spinS transverse
Ising model with vanishing or nonvanishing parallel external field,
the BlumeEmeryGriffiths model and the BlumeCapel model, mixed
spin and mixed bond periodic systems such as alternating Ising chains
or Ising ferrimagnets and also includes Ising models with random structures.
Low temperature behaviors of these systems and the crossover to infinite
spin systems are also investigated.
Kazuhiko Minami:
The exact susceptibility of the transverse Ising chain and Ising type chains with arbitrary spin
J.Mag.Mag.Mat. 177181 (1998) 165166, proceedings
Masayuki Hagiwara, Yasuo Narumi, Kazuhiko Minami, Keiji Tatani and Koichi Kindo:
Magnetization process of the s=1/2 and 1 ferrimagnetic chain and dimer
J.Phys.Soc.Jpn.68 (1999) 22142217
Masayuki Hagiwara, Yasuo Narumi, Kazuhiko Minami and Koichi Kindo:
Highfield magnetization of an s=1/2 FFAFAF tetramer chain
Physica B294295 (2001) 3033
Masayuki Hagiwara, Kazuhiko Minami and Hiroko Aruga Katori:
Thermodynamic properties of a quantum ferrimagnet formed by
an S=1/2 tetramer chain
Prog. Theor. Phys. 145 (2002) 150155
Masayuki Hagiwara, Yasuo Narumi, Kazuhiko Minami, Koichi Kindo,
Hideaki Kitazawa, Hiroyuki Suzuki, Naoto Tsuji and Hideki Abe:
Magnetization process of an S=1/2 tetramer chain with
ferromagneticferrimagneticantiferromagnetic bond alternating interactions
J.Phys.Soc.Jpn. 72 (2003) 943946
Kazuhiko Minami:
On the saturation field of magnets
J. Mag. Mag. Mat. 270 (2004) 104118
Jozef Strecka, Michal Jascur, Masayuki Hagiwara, Kazuhiko Minami:
Magnetic properties of a tetramer ferroferroantiferroantiferromagnetic IsingHeisenberg bond alternating chain as a model system for Cu(3Clpy)2(N3)2
Czech. J. Phys, 54 Suppl 4 (2004) 583586, proceedings, condmat/0406680
Kazuhiko Minami:
An equivalence relation of boundary/initial conditions and the infinite limit properties
J. Phys. Soc. Jpn. 74 (2005) 16401641
,
condmat/0503192

Abstract:
The 'nequivalences' of boundary conditions of lattice models are introduced and it is derived that the models with nequivalent boundary conditions result in the identical free energy. It is shown that the free energy of the sixvertex model is classified through the density of left/down arrows on the boundary. The free energy becomes identical to that obtained by Lieb and Sutherland with the periodic boundary condition, if the density of the arrows is equal to 1/2. The relation to the structure of the transfer matrix and a relation to stochastic processes are noted.
Jozef Strecka, Michal Jascur, Masayuki Hagiwara, Kazuhiko Minami,
Yasuo Narumi and Koich Kindo:
Thermodynamic properties of a tetramer IsingHeisenberg bond alternating
chain as a model system for Cu(3Chloropyridine)2(N3)2
Phys.Rev.B72 (2005) 024459 (111), condmat/0406680
南 和彦: 「統計力学、フラクタル、そして格子模型」
数理科学2006年5月号（サイエンス社）
Kazuhiko Minami:
The free energies of sixvertex models and the nequivalence relation
J. Math. Phys. 49 (2008) 033514
,
condmat/0607513

Abstract:
The free energies of sixvertex models on general domain D with various boundary conditions are investigated with the use of the nequivalence relation which classifies the thermodynamic limit properties. It is derived that the free energy of the sixvertex 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.
Jozef Strecka, Lucia Canova and Kazuhiko Minami:
Spin1/2 IsingHeisenberg model with the pair XYZ Heisenberg interaction and quartic Ising
interactions as the exactly soluble zerofield eightvertex model
Phys.Rev.E 79 (2009) 051103
Erratum: Phys.Rev.E 83 (2011) 069904(E)
Jozef Strecka, Lucia Canova and Kazuhiko Minami:
Weak universal critical behavior and quantum critical point
of the exactly soluble spin1/2 IsingHeisenberg model
with the pair XYZ Heisenberg and quartic Ising interactions
AIP Conf. Proc. 1198 (2009) 156165
南 和彦: 「微分積分講義」(裳華房, 2010)
Kazuhiko Minami:
Fractal structure of a solvable lattice model
Int. J. Pure and Applied Math., 59 (2010) 243255
,
condmat/0801.0186

Abstract:
Fractal structure of the sixvertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the sixvertex model. It is pointed out that the transfer matrix method and the nequivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can be generalized for the models suitable to the transfer matrix treatment, and hence this gives general relation between solvable lattice models and fractal geometry.
南 和彦:
格子模型の厳密解と生態系
京都大学数理科学研究所講究録 1704 (2010) 158164.
曾根彰吾、久保勲生、南 和彦:
Hopfield模型における誤りとノイズの効果
京都大学数理科学研究所講究録 1706 (2010) 1725.
L. Allen著「生物数学入門」
竹内・佐藤・宮崎・守田 他と共訳 共立出版(2011)
Kazuhiko Minami:
Equivalence between twodimensional cellsorting and onedimensional generalized random walk
spin representations of generating operators.
arXiv:1106.6210v1 [qbio.CB]

Abstract:
The twodimensional cellsorting problem is found to be mathematically
equivalent to the onedimensional random walk problem with pair creations and
annihilations, i.e. the adhesion probabilities in the cellsorting model relate
analytically to the expectation values in the random walk problem. This is an
example demonstrating that two completely different biological systems are
governed by a common mathematical structure. This result is obtained through
the equivalences of these systems with lattice spin models. It is also shown
that arbitrary generation operators can be written by the spin operators, and
hence all biological stochastic problems can in principle be analyzed utilizing
the techniques and knowledge previously obtained in the study of lattice spin
systems.
勝又紘一、南 和彦：「量子スピン系、実験」
川端・鹿児島・北岡・上田 編「物性物理ハンドブック」朝倉書店(2012)
南 和彦:
細胞選別ランダムウォークの等価性と生体内の１次元確率過程
京都大学数理科学研究所講究録 1796 (2012) 7280.
Kazuhiko Minami:
Exact transverse susceptibility of onedimensional random bond
Ising model with alternating spin.
J. Phys. A: Math. Theor. 46 (2013) 505005.
南 和彦 「格子模型の数理物理」
SGCライブラリ108 別冊数理科学 (サイエンス社 2014)
Kazuhiko Minami:
Equivalence between the twodimensional Ising model and the quantum XY chain
with randomness and with open boundary.
Europhys. Lett., 108 (2014) 30001.
,
arXiv:1209.2442 [condmat.statmech]

Abstract:
It is derived that the twodimensional Ising model with alternating/random interactions and with periodic/free boundary conditions is equivalent to the ground state of the onedimensional alternating/random XY model with the corresponding periodic/free boundary conditions.
This provides an exact equivalence between a random rectangular Ising model,
in which the GriffithsMcCoy phase appears, and a random XY chain.
Kazuhiko Minami:
Solvable Hamiltonians and fermionization transformations
obtained from operators satisfying specific commutation relations,
J. Phys. Soc. Jpn. 85, 024003 (2016).

Abstract:
It is shown that a solvable Hamiltonian can be obtained
from a series of operators satisfying specific commutation relations.
A transformation that diagonalize the Hamiltonian
is obtained simultaneously.
The twodimensional Ising model with periodic interactions,
the onedimensional XY model with period 2,
the transverse Ising chain,
the onedimensional Kitaev model and the cluster model,
and other composite quantum spin chains
are diagonalized following this procedure.
The JordanWigner transformation,
the transformation from the Pauli spin operators to the Majorana fermion
used by Shankar and Murthy,
and the transformation introduced by Nambu,
are special cases of this treatment.
Kazuhiko Minami:
Infinite number of solvable generalizations of XYchain,
with cluster state,
and with central charge c=m/2,
Nuclear Physics B, 925 (2017) 144160.
,
arXiv:1710.01851.

Abstract:
An infinite number of spin chains are solved and it is derived
that the groundstate phase transitions belong to the universality classes
with central charge c=m/2, where m is an integer.
The models are diagonalized by automatically obtained transformations,
many of which are different from the JordanWigner transformation.
The free energies, correlation functions, string order parameters,
exponents, central charges, and the phase diagram are obtained.
Most of the examples consist of the stabilizers of the cluster state.
A unified structure of the onedimensional XY and clustertype spin chains is revealed,
and other series of solvable models can be obtained
through this formula.
Kazuhiko Minami:
Honeycomb lattice Kitaev model with WenToriccode interactions,
and anyon excitations,
Nuclear Physics B, 939 (2019) 465484.
,
arXiv:1710.01851.

Abstract:
The honeycomb lattice Kitaev model H_K
with two kinds of WenToriccode fourbody interactions H_WT
is investigated exactly
using a new fermionization method,
and the ground state phase diagram is obtained.
Six kinds of threebody interactions are also considered.
A Hamiltonian equivalent to the honeycomb lattice Kitaev model
is also introduced.
The fermionization method is generalized to twodimensional systems,
and the twodimensional JordanWigner transformation is obtained
as a special case of this formula.
The model H_K+H_WT is symmetric
in fourdimensional space of coupling constants,
and the anyon type excitations appear in each phase.
南 和彦: 「線形代数講義」(裳華房, 2020)
Yuji Yanagihara and Kazuhiko Minami:
Exact solution of cluster model with nextnearestneighbor interaction,
Prog. Theor. Exp. Phys. 2020.11 (2020): 113A01.
,
arXiv:2003.00962.
Masahiro Ogura, Yukihisa Imamura, Naruhiko Kameyama, Kazuhiko Minami, and Masatoshi Sato:
Geometric Criterion for Solvability of Lattice Spin Systems,
Phys. Rev. B 102, 245118 (2020).
,
arXiv:2003.13264.

Abstract:
We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of adjacency matrices of the graphs provide conserved quantities of the systems. Furthermore, when the graphs belong to a class of simplicial complexes, the Hamiltonians are found to be mapped to bilinear forms of Majorana fermions, from which the full spectra of the systems are obtained. In the latter situation, we find a relation between conserved quantities and the first homology group of the graph, and the relation enables us to interpret the conserved quantities as flux excitations of the systems. The validity of our theory is confirmed in several known solvable spin systems including the 1d transversefield Ising chain, the 2d Kitaev honeycomb model and the 3d diamond lattice model. We also present new solvable models on a 1d trijunction, 2d and 3d fractal lattices, and the 3d cubic lattice.
Kazuhiko Minami:
Onsager algebra and algebraic generalization of JordanWigner transformation,
Nucl. Phys. B 973, 115599 (2021).
,
arXiv:2108.03811.

Abstract:
Recently, an algebraic generalization of the JordanWigner transformation
was introduced and applied to one and twodimensional systems.
This transformation is composed of the interactions ¥eta_i
that appear in the Hamiltonian H
as H=∑ J_i ¥eta_i,
where J_i are coupling constants.
In this short note,
it is derived that
operators that are composed of ¥eta_i,
or its nstate clock generalizations,
satisfy the DolanGrady condition
and hence obey the Onsager algebra
which was introduced in the original solution of the rectangular Ising model
and appears in some integrable models.
Kazuhiko Minami:
The exact susceptibility of the spinS transverse Ising chain with nextnearestneighbor interactions,
J.Phys.Soc.Jpn.92, 054001 (2023).
,
arXiv:2212.12693.

Abstract:
The zerofield susceptibility
of the spin$S$ transverse Ising chain
with nextnearestneighbor interactions
is obtained exactly.
The susceptibility is given in an explicit form for $S=1/2$,
and expressed in terms of the eigenvectors of the transfer matrix
for general spin $S$.
It is found that the lowtemperature limit is independent of spin $S$,
and is divergent at the transition point.
Kazuhiko Minami:
Conserved Charges of Series of Solvable Lattice Models,
arXiv:2410.20798.
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