Prog. Theor. Phys. Vol. 37 No. 2 (1967) pp. 276-295

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Generalized Theory of Condensing Systems. V

— Some Remarks on the Validity of the G-Condition —

Kazuyosi Ikeda

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

(Received September 26, 1966)

Abstract:

Discussions are given of the validity of the G-condition, which was used as the starting point of the theory of condensing systems in the author's previous papers, and which was considered to represent the essential features of the volume-dependent cluster integrals of the physical real systems. In particular, for classical systems with two-body forces of finite range, the concept of “maximum length” of a cluster is introduced, and, with the use of this, some theorems are established which are useful for testing the validity of (G·3) [which is the third item of the G-condition and assumes the independence, upon u (volume per moelcule), of the contribution per molecule to the (infinitely large) cluster integral in some range of values of u]. The validitiy of the assumptions in the theorems is discussed from the physical point of view. In this connection, some arguments are made about the analytical properties of the condensation point, strongly supporting the identity of the condensation point of the classical real system and that of the (0)-system (i. e. the system consisting of volume-independent cluster integrals). Some remarks are given on the G-condition in the case of the general system (quantal or classical). Finally, analytical examples of functions satisfying the G-condition are shown.

URL : http://ptp.ipap.jp/link?PTP/37/276/
DOI : 10.1143/PTP.37.276

References:

K. Ikeda, Prog. Theor. Phys. 26 (1961), 173[PTP]; reprinted in Prog. Theor. Phys. Suppl. No. 34 (1965), 6[PTP]; referred to as paper I.
K. Ikeda and T. Nakazawa, Lecture at the meeting of the Physical Society of Japan held at Nagyoa University on October 18, 1960; Prog. Theor. Phys. Suppl. No. 34 (1965), 91[PTP]; referred to as paper III.
K. Ikeda, Prog. Theor. Phys. (preceding paper in this issue), referred to as paper IV.
K. Ikeda, Proc. Internat'l Conf. Theor. Phys. Kyoto and Tokyo (1953), p. 544.
K. Ikeda, Prog. Theor. Phys. 16 (1956), 341 [PTP](containing the complete proofs of the lemmata and theorems given in reference 4)).
H. Fujita and S. Katsura, Sci. Rep. Tohoku Univ. Ser. I, 35 (1952), 206.
J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, 1940), Chap. 13.
K. Ikeda, Prog. Theor. Phys. 11 (1954), 336[PTP].
K. Ikeda, Prog. Theor. Phys. 19 (1958), 653[PTP].

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