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Prog. Theor. Phys. Vol. 53 No. 3 (1975) pp. 634-645

[ Full Text PDF : FREE ACCESS (710K) ]

Volume-Dependent Cluster Sums for Lattice Cases. II

— Prototypes of Seven or Eight Points —

Kunisuke Nisizima and Kazuyosi Ikeda

Department of Applied Physics, Faculty of Engineering, Osaka University, Suita, Osaka

(Received June 8, 1974)

Abstract:

In order to calculate the Temperley coefficients cm for m=7, 8 (and consequently the volume-dependent cluster sums involving seven or eight particles) for lattice gases with nearest-neighbour interactions by means of method of a preceding paper I, all the prototypes (defined in I) of seven or eight points are described and their values are calculated. Since the value of a prototype is the sum of the values of all the formal diagrams (defined in I) derived from it, some examples of formal diagrams and their values are given. The values are expressed as hypercomplex numbers, by which the three-dimensional (simple cubic), two-dimensional (square) and one-dimensional lattices are simultaneously represented.


URL : http://ptp.ipap.jp/link?PTP/53/634/
DOI : 10.1143/PTP.53.634

[ Full Text PDF : FREE ACCESS (710K) ] Citation:

References:

  1. K. Ikeda and K. Nisizima, Prog. Theor. Phys. 53 (1975), 326[PTP]; referred to as I.

Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 3499-3511 :
    Cluster Sums for Lattice Gases with Second Nearest Neighbour Interactions. III. Three-Dimensional Simple Cubic Lattice
    Kunisuke Nisizima and Kazuyosi Ikeda
  2. Journal of the Physical Society of Japan 61 (1992) pp. 1520-1526 :
    Volume-Dependent Cluster Sums and Phase Transition of the Two-Dimensional Triangular Lattice Gas
    Kazuyosi Ikeda and Kunisuke Nisizima
  3. Journal of the Physical Society of Japan 61 (1992) pp. 1527-1534 :
    Volume-Dependent Irreducible Cluster Sums and Phase Transition of Lattice Gases
    Kunisuke Nisizima and Kazuyosi Ikeda
  4. Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1056-1072 :
    Volume-Dependent Cluster Sums for Lattice Gases. III
    Kazuyosi Ikeda and Kunisuke Nisijima
  5. Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1343-1345 :
    Volume-Dependent Cluster Sums for Lattice Gases. IV
    Kunisuke Nisizima and Kazuyosi Ikeda
  6. Progress of Theoretical Physics Vol. 71 No. 4 (1984) pp. 689-706 :
    Phase Transitions of Lattice Gases
    Kunisuke Nisizima and Kazuyosi Ikeda

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