High Temperature Expansion for the Ising Model on the Penrose Lattice

Ryuzo Abe and Tomonari Dotera

J. Phys. Soc. Jpn. 58 (1989), pp.3219-3226

High temperature expansion for ln Z (Z: the partition function in the absence of magnetic field) of the Ising model on the Penrose lattice is discussed. The terms up to the order of w8 are derived. To illustrate an extrapolation procedure employed here, the critical compressibility factor Zc and the correlation function C at Tc, for the neighboring spin pair are first treated in the case of two-dimensional square lattice. It turns out that the terms up to w8 for ln Z lead to the results within the error of 0.2 ~ 0.30% as compared to exact values. Along the same line, Zc and C (average correlation function) are calculated for the Penrose lattice. The final results are Zc=0. 138+-0.002 and C=0.673+-0.003.

Keywords: high temperature expansion, Ising model, Penrose lattice, critical phenomena, theory