Distribution of Zeros and the Equation of State. I : Fundamental Relations and a Theorem on a Cauchy-Type Integral
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The fundamental relations between the distribution, in the complex z(=activity) plane, of the zeros of the grand partition function (for a system of infinitely large volume) and the equation of state are discussed; for linear distribution, an analysis of a Cauchy-type integral leads to a theorem which connects discontinuities of the distribution function or its derivative of some order with singularities of the thermodynamic functions (of complex z). Relations between the distribution of zeros on a circle (with centre at the origin) and the equation of state are also discussed; in particular, it is proved that if the distribution function on the circle is increasing, the density of the system as a function of (real) z is increasing. This paper serves as a preliminary argument for the investigation of the phase transitions in some examples of circular distribution in a subsequent paper.
- 理論物理学刊行会の論文
- 1977-08-25
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