List of Publications

Kazuhiko Minami, Yoshihiko Nonomura, Makoto Katori and Masuo Suzuki:
Multi-effective-field theory: applications to the CAM analysis of the two-dimensional Ising model
Physica A174 (1991) 479-503

Kazuhiko Minami and Masuo Suzuki:
Coherent-anomaly method applied to the eight-vertex model
Physica A187 (1992) 282-307

Kazuhiko Minami and Masuo Suzuki:
Non-universal critical behaviour of the two-dimensional Ising model with crossing bonds
Physica A192 (1993) 152-166

Kazuhiko Minami and Masuo Suzuki:
A two-dimensional Ising model with non-universal critical behaviour
Physica A195 (1993) 457-473

Kazuhiko Minami and Masuo Suzuki:
Non-universal critical behaviour of two-dimensional Ising models via two-body interactions
Phys. Lett. A180 (1993) 179-182

Abstract: The square-lattice Ising model with antiferromagnetic next-nearest-neighbour interaction and the Ising models with the four-body 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:
Non-universal critical behaviour of two-dimensional Ising systems
J. Phys. A: Math. Gen. 27 (1994) 7301-7311 , cond-mat/0404572

Abstract: Two conditions are derived for Ising models to show non-universal 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 eight-vertex model, the Ashkin-Teller model, some Ising models with short- or long-range interactions and even Ising systems without the translational or the rotational invariance.

Masuo Suzuki, Kazuhiko Minami and Yoshihiko Nonomura:
Coherent-anomaly method -- recent development
Physica A205 (1994) 80-100, proceedings

Masuo Suzuki, Xiao Hu, Makoto Katori, Adam Lipowski, Naomichi Hatano, Kazuhiko Minami and Yoshihiko Nonomura:
Coherent-Anomaly 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 linear-chain Heisenberg antiferromagnet CsV1-xMgxCl3
J. Phys. Cond.Mat. 8 (1996) 8407-8412

Kazuhiko Minami:
The zero-field susceptibility of the transverse Ising chain with arbitrary spin
J. Phys. A: Math. Gen. 29 (1996) 6395-6405

Abstract: The zero-field susceptibility of the transverse Ising chain with arbitrary spin-S 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 zero-temperature limit of the susceptibility is independent of spin-S.

Hitoshi Asakawa, Masaaki Matsuda, Kazuhiko Minami, Hideki Yamazaki and Kouichi Katsumata:
Experimental and theoretical approach to finite-size effects in an S=1/2 antiferromagnetic Heizenberg open chain
Phys.Rev.B57 (1998) 8285-8289

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) 2209-2211, cond-mat/9807348

Kazuhiko Minami:
The susceptibility in arbitrary directions and the specific heat of general Ising-type chains with uniform, periodic and random structures
J.Phys.Soc.Jpn. 67 (1998) 2255-2269

Abstract: The susceptibility in arbitrary directions, the specific heat, the energy and the magnetization of general Ising-type chains are exactly expressed in terms of the eigenvectors of the transfer matrix corresponding to the Ising-type 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 spin-S transverse Ising model with vanishing or non-vanishing parallel external field, the Blume-Emery-Griffiths model and the Blume-Capel 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 trnasverse Ising chain and Ising type chains with arbitrary spin
J.Mag.Mag.Mat. 177-181 (1998) 165-166, 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) 2214-2217

Masayuki Hagiwara, Yasuo Narumi, Kazuhiko Minami and Koichi Kindo:
High-field magnetization of an s=1/2 F-F-AF-AF tetramer chain
Physica B294-295 (2001) 30-33

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) 150-155

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 ferromagnetic-ferrimagnetic-antiferromagnetic bond alternating interactions
J.Phys.Soc.Jpn. 72 (2003) 943-946

Kazuhiko Minami:
On the saturation field of magnets
J. Mag. Mag. Mat. 270 (2004) 104-118

Jozef Strecka, Michal Jascur, Masayuki Hagiwara, Kazuhiko Minami:
Magnetic properties of a tetramer ferro-ferro-antiferro-antiferromagnetic Ising-Heisenberg bond alternating chain as a model system for Cu(3-Clpy)2(N3)2
Czech. J. Phys, 54 Suppl 4 (2004) 583-586, proceedings, cond-mat/0406680

Kazuhiko Minami:
An equivalence relation of boundary/initial conditions and the infinite limit properties
J. Phys. Soc. Jpn. 74 (2005) 1640-1641 , cond-mat/0503192

Abstract: The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex 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 Ising-Heisenberg bond alternating chain as a model system for Cu(3-Chloropyridine)2(N3)2
Phys.Rev.B72 (2005) 024459 (1-11), cond-mat/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 six-vertex models and the n-equivalence relation
J. Math. Phys. 49 (2008) 033514 , cond-mat/0607513

Abstract: 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.

Jozef Strecka, Lucia Canova and Kazuhiko Minami:
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
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 spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg and quartic Ising interactions
AIP Conf. Proc. 1198 (2009) 156-165

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) 243-255 , cond-mat/0801.0186

Abstract: Fractal structure of the six-vertex 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 six-vertex model. It is pointed out that the transfer matrix method and the n-equivalence 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) 158-164.

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) 17-25.

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 two-dimensional cell-sorting and one-dimensional generalized random walk
--spin representations of generating operators--.
arXiv:1106.6210v1 [q-bio.CB]

Abstract: The two-dimensional cell-sorting problem is found to be mathematically equivalent to the one-dimensional random walk problem with pair creations and annihilations, i.e. the adhesion probabilities in the cell-sorting 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) 72-80.

Kazuhiko Minami:
Exact transverse susceptibility of one-dimensional 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 two-dimensional Ising model and the quantum XY chain with randomness and with open boundary.
Europhys. Lett., 108 (2014) 30001. , arXiv:1209.2442 [cond-mat.stat-mech]

Abstract: It is derived that the two-dimensional Ising model with alternating/random interactions and with periodic/free boundary conditions is equivalent to the ground state of the one-dimensional 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 Griffiths-McCoy 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 two-dimensional Ising model with periodic interactions, the one-dimensional XY model with period 2, the transverse Ising chain, the one-dimensional Kitaev model and the cluster model, and other composite quantum spin chains are diagonalized following this procedure. The Jordan-Wigner 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 XY-chain, with cluster state, and with central charge c=m/2,
Nuclear Physics B, 925 (2017) 144-160. , arXiv:1710.01851.

Abstract: An infinite number of spin chains are solved and it is derived that the ground-state 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 Jordan-Wigner 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 one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

Kazuhiko Minami:
Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations,
Nuclear Physics B, 939 (2019) 465-484. , arXiv:1710.01851.

Abstract: The honeycomb lattice Kitaev model H_K with two kinds of Wen-Toric-code four-body interactions H_WT is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan-Wigner transformation is obtained as a special case of this formula. The model H_K+H_WT is symmetric in four-dimensional 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 next-nearest-neighbor 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 transverse-field Ising chain, the 2d Kitaev honeycomb model and the 3d diamond lattice model. We also present new solvable models on a 1d tri-junction, 2d and 3d fractal lattices, and the 3d cubic lattice.

Kazuhiko Minami:
Onsager algebra and algebraic generalization of Jordan-Wigner transformation,
Nucl. Phys. B 973, 115599 (2021). , arXiv:2108.03811.

Abstract: Recently, an algebraic generalization of the Jordan-Wigner transformation was introduced and applied to one- and two-dimensional 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 n-state clock generalizations, satisfy the Dolan-Grady 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 spin-S transverse Ising chain with next-nearest-neighbor interactions,
J.Phys.Soc.Jpn.92, 054001 (2023). , arXiv:2212.12693.

Abstract: The zero-field susceptibility of the spin-$S$ transverse Ising chain with next-nearest-neighbor 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 low-temperature limit is independent of spin $S$, and is divergent at the transition point.