Prog. Theor. Phys. Vol. 84 No. 3 (1990) pp. 425-435
Critical Compressibility Factor of Two-Dimensional Lattice Gas
— Kagomé and Diced Lattices
Department of Pure and Applied Sciences,
University of Tokyo, Komaba, Tokyo 153
(Received May 17, 1990)
The critical compressibility factor Zc at the gas-liquid critical point is defined by Zc=pcVc/NkBTc (pc: critical pressure, Vc: critical volume, Tc: critical temperature, kB: Boltzmann's constant, N: number of molecules). The Zc of the lattice gas on the Kagomé or diced lattice is discussed. First, on the basis of exact solution for the partition function Z of the Ising model without magnetic field on these lattices, the Zc is calculated exactly. The results are Zc=0.08330842 … (Kagomé lattice) and Zc=0.14284554 … (diced lattice). Secondly, high temperature expansion for Zc is studied and the expansion is carried out up to w13 for the Kagpmé lattice and up to w12 for the diced lattice. Extrapolation procedures for obtaining Zc are discussed. A similarity between the diced and Penrose lattices and the one between the Kagomé and dual Penrose lattices are pointed out.
DOI : 10.1143/PTP.84.425
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Citing Article(s) :
Progress of Theoretical Physics Vol. 85 No. 3 (1991) pp. 509-525
Zeros of Partition Function and High Temperature Expansion for the Two-Dimensional Ising Models
Ryuzo Abe, Tomonari Dotera and Takeshi Ogawa