On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. I : Fundamental Concepts and the Limit of Vanishing Attraction
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Some fundamental concepts concerning the distribution of zeros of the grand partition function on the complex z (activity) plane are described. In order to obtain a unique distribution of zeros from the knowledge of the equation of state, we assume that the zeros are distributed on lines and the equation of state is analytically continued as far as possible in the complex plane. As an example, the distribution of zeros for a gas obeying van der Waals' equation of state, in the limit of vanishing attraction, is investigated. The Riemann surface of the pressure considered as a function of z is constructed. The line of zeros is determined from it as the "jumping line" between two sheets, which is a part of the negative real axis. The distribution function for zeros on the line is obtained. Though the problem treated in this paper has already been investigated by Hauge and Hemmer, the method of this paper including the analysis of the Riemann surface is useful in the arguments of the more complicated cases in the subsequent papers.
- 理論物理学刊行会の論文
- 1974-07-25
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