Distribution of Zeros and the Equation of State. III : Cluster Series, the Ideal Fermi-Dirac Gas and Other Problems
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The radius of convergence of the cluster series (expressing the equation of state) is discussed in connection with the distribution of zeros of the grand partition function on the complex z (= activity) plane, by giving various examples of circular distribution. Anomalous phase transitions and phase transitions of third order are considered by showing some examples of circular distribution of zeros. For the ideal Fermi-Dirac gas, the distribution function of zeros, lying on the part of the negative real axis from -λ^<-3> to -∞ [where λ= h(2πmkT)^<1/2> ], is calculated, and the function-theoretical structure of the equation of state is investigated. The distribution of zeros for this gas is compared with that for Tonks' gas (having purely repulsive interparticle forces). The two-dimensional and one-dimensional Fermi-Dirac gases are dealt with from the point of view of the distribution of zeros.
- 理論物理学刊行会の論文
- 1982-08-25
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