Computer No.53 (1992) IBM 650. Bacon TSS JRR-2.[1] free inductin decay IBM 7044 FACOM

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1 Computer No.53 (1992) IBM Bacon IBM 650 TSS JRR-2.[1] 2 43 IBM FACOM Abragam CaF 2 free inductin decay IBM 7044 FACOM

2 S34-47 [2-5] FACOM S48-52 [6-8] FACOM S51-56 [9-12] FACOM F75APU M200 S56-61 [13-16] M200 M380 VP100 S58-63 [17-28] M380 M780 VP100 job Physical Review Letters.[5].[8] 50 JRR-2 DMNS HITAC 10 on-line HITAC 10 8K CTNS (1) GPL HITAC 10 (2) HITAC 10 (3) HITAC 10 8K TAS-II 3 2

3 KENO-IV IBM 7044 FACOM FASM 50.[9] rounding A(1 T /T c ) β T c β CAM rounding [12] 56 F75APU Array Processor Unit ±J single spin flip N 2 N 3

4 N Morgenstern Binder recursive method 57 N 2 N 2 N N (recursively) 2 N DIMENSION ±J.[13].[14] VP100 SPIN 15 job DIMENSION VP100 32MB MB FACOM DIMENSION Memory is time. SPIN [15] SPIN FORTRAN77EX SPIN N N 2m m N 2 N 2 2m 4

5 m 2 m 2 XY m 2 Physical Review Letters.[17].[18-28] 59 61, 62 6 N 2 N N S (2S + 1) N Z N S (1) = 0 XY ; (2) = 0.5 ; (3) = 1 Haldane S = 0.5 S = 1 = 0.5.[25] S = 2 1 = 0.5 crossover.[26] S = Haldane 61 IBM Bednorz Müller 62 CuO 2 VP MB VP2600 VP VP100 N S Betts S S= 1 2 (26), 1(16), 3 2 (10), 2(10), 2 5 (8), 3(8). N S N S 5

6 S 2 XY ( =0 0.4) xy ( = ) zz ( = ) crossover S 2dS= 1 2 1dS=1 1dS=1 VBS 2dS= 2 1 RVB 2dS=1 1dS=2 2dS= 2 3 1dS=3 1dS= 1 2 1dS= 1 2 Haldane 1dS=1 1dS= 2 1 1dS= 1 2.[29] S= MB VP GB ATF PTS NLP 100% LATEX+REVTEX REVTEX Physical Review bitnet PDS Ngraph 49 TSS 6

7 S N (2S + 1) N S N (2S + 1) N MB 1h19m s h32m s m s m m m m [*] [1] N. Kunitomi, M. Sakamoto, Y. Hamaguchi and H. Betsuyaku: Reflectivity of Collimated Neutrons by a Mosaic Single Crystal, J. Phys. Soc. Jpn. 19 (l964) [2] H. Betsuyaku: Calculation of 14 N Quadrupole Constant in the Nitrite Ion, J. Chem. Phys. 50 (1969) NO 2-14 N CNDO [3] [3] H. Betsuyaku: Calculation of the Charge Distribution and Orbital Energies of the Ground State of the Nitrite Ion, J. Chem. Phys. 50 (1969) NO 2 - x [4] H. Betsuyaku: Charge Distribution and Nuclear Quadrupole Interactions in Ionic Crystals, J. Chem. Phys. 51 (1969) NaNO 2 Planewise Lattice Summation [5] H. Betsuyaku: Lowe-Norberg Theory of Nuclear-Magnetic-Resonance Free Induction Decay in Solids, Phys. Rev. Lett. 24 (1970) 934. CaF 2 43 IBM FACOM IBM 7044 FACOM [6] H. Betsuyaku and Y. Hamaguchi: Neutron Scattering Investigation of Magnetic Excitations in KMnF 3, J. Phys. Soc. Jpn. 37 (1974) 975. KMnF 3 KMnF 3 7

8 JRR-2 [7] H. Betsuyaku: Neutron Scattering Function in a Heisenberg Paramagnet: Application to KMnF 3, J. Phys. Soc. Jpn. 38 (1975) 21. Kadanoff-Martin sum-rule moment KMnF 3 [6] [8], 18 (1977) p.181. DMNS HITAC 10 VAX [9] H. Betsuyaku: A New Monte Carlo Calculation of the Magnetization of a Classical Heisenberg Ferromagnet, Phys. Lett. 64A (1977) 98. rounding A(1 T /T c ) β β [10] H. Betsuyaku: Monte Carlo Investigation of Magenetic Properties of a Two-Dimensional Classical Heisenberg Magnet, Solid State Commun. 25 (1978) 185. Mermin-Wigner [11] H. Betsuyaku: Monte Carlo Investigation of Magenetic Properties of a Two-Dimensional Plane-Rotator Model, Solid State Commun. 25 (1978) 829. Zittartz [12] H. Betsuyaku: Monte Carlo Realization of Kadanoff Block Transformation in the 2d Plane-Rotator Model, Physica 106A (1981) [13] H. Betsuyaku: Spin-Glass Properties of ±J Random-Bond Model, J. Magn. Magn. Mat (1983) [14] H. Betsuyaku: New Type of Phase Transition in the 2-d Ising Model with regularly Disposed Frustration, J. Phys. Soc. Jpn. 52 (1983) Suppl

9 [15], JAERI-M (1987) p.99. SPIN SPIN [16] H. Betsuyaku: Thermodynamics of the Two-Dimensional Ising Model with Regularly Disposed Frustrations, Progr. Theor. Phys. Suppl. No. 87 (l986) 43. Vdovichenko EISPACK Onsager [17] H. Betsuyaku: Study of One-Dimensional XY Model by the Transfer-Matrix Method, Phys. Rev. Lett. 53 (1984) 629. XY [18] H. Betsuyaku: Study of One-Dimensional Quantum Spin System by the Transfer-Matrix Method, Prog. Theor. Phys. 73 (1985) 319. [19] T. Yokota and H. Betsuyaku: Study of One-Dimensional Fermion Model by the Transfer-Matrix Method, Prog. Theor. Phys. 75 (1986) 46. [20] H. Betsuyaku: Cluster Transfer-Matrix Method for One-Dimensional Quantum Spin Systems, Prog. Theor. Phys. 75 (1986) 774. [21] H. Betsuyaku and T. Yokota: Study of One-Dimensional Quantum Spin System by the Transfer-Matrix Method. II S=1 Case, Prog. Theor. Phys. 75 (1986) 808. [22] H. Betsuyaku and T. Yokota: Ground State of Antiferromagnetic Heisenberg Rings Studied by the Projector Method, Phys. Rev. B 33 (1986) [24-26] 9

10 [23] M. Suzuki and H. Betsuyaku: Thermofield Transfer-Matrix Method and its Applications to Quantum Spin Systems, Phys. Rev. B 34 (l986) [24] H. Betsuyaku: Finite-Lattice Extrapolations for the Ground-State Energies of Antiferromagnetic Heisenberg Rings, Phys. Rev. B 34 (l986) Vanden Broeck Schwartz S= 2 1 XY S=1 [25] H. Betsuyaku: Magnons and Solitons in a Spin-1 Antiferromagnetic Heisenberg-Ising Ring, Phys. Rev. B 36 (l987) 799. S=1 Haldane [26] H. Betsuyaku: Crossover Effects in a Spin- 1 2 Antiferromagnetic Heisenberg-Ising Ring, Phys. Rev. B 36 (l987) S= 2 1 Crossover [27] H. Betsuyaku: Qauantum Transfer-Matrix Method and its Applications to Quantum Spin Systems, in Quantum Monte Carlo Methods, edited by M. Suzuki (Springer, Berlin, 1987), pp Suzuki-Trotter [28], 42 (1987) 161. [29],

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