Critical Compressibility Factor of Two-Dimensional Lattice Gas - *Kagome and Diced Lattices*-

Ryuzo Abe, Tomonari Dotera and Takeshi Ogawaa

Prog. Theor. Phys. **84 **(1990), pp.425-435

The critical compressibility factor *Zc* at the gas-liquid critical point is defined by *Zc*=*pcVc*/*Nk*B*Tc* (*pc*: critical pressure, *Vc*: critical volume, *Tc*: critical temperature, *k*B: Boltzmann's constant, *N*: number of molecules). The *Zc* of the lattice gas on the Kagome 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**... **(Kagome lattice) and *Zc*=0.14284554**...** (diced lattice). Secondly, high temperature expansion for *Zc *is studied and the expansion is carried out up to *w*13 for the Kagome lattice and up to *w*12 for the diced lattice. Extrapolation procedures for obtaining *Zc* are discussed. A similarity between the diced and Penrose lattices and the one between the Kagome and dual Penrose lattices are pointed out.