High Temperature Expansion for the Ising Model on the Dual Penrose Lattice

Tomonari Dotera and Ryuzo Abe

J. Phys. Soc. Jpn. 59 (1990), pp.2064-2077

High temperature expansion for ln Z(Z : the partition function in the absence of a magnetic field) of the Ising model on the dual Penrose lattice is discussed. The terms up to w10 are derived by using projection method. The critical compressibility factor Zc and the average correlation function C are calculated in terms of duality relation. The final results are Zc = 0.0846 +-0.007 and C= 0.7403+-0.0024, which are confirmed by the expansion. Lattice constants are shown in some tables.

Keywords: critical phenomena, critical compressibility factor, dual Penrose lattice, duality, high temperature expansion, Ising model, lattice constant, projection method, theory