On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. III : Calculations for Low Temperatures

概要

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With the use of the arguments in paper II, the distribution of zeros of the grand partition function for a gas obeying van der Waals' equation of state is calculated for temperatures low compared with the critical temperature. Two expressions of the pressure as a function of the activity are found which are valid, respectively, in the Riemann sheet involving the gaseous phase and the one involving the liquid phase. As "jumping line" between these two sheets the line of zeros, which is a closed curve enclosing the origin, is obtained. The distribution function for zeros on this line is also calculated. The formulae obtained are correct as long as one neglects O(α^<-7>) and O(α^<-4>e^<-α>) as compared with 1, where α≡a/b^2kT (a,b being constants depending on the substance). Also the part of the negative real axis to the left of the point of intersection of the closed curve and the real axis is a zero line; the distribution function for zeros on this line is calculated, with O{α^<-4>(lnα)^4} neglected as compared with 1. Comparison is made with Hemmer and Hauge's rough calculations.
理論物理学刊行会の論文
1974-09-25