## Abstracts

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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

### Abstract

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 *w*8 are derived. To illustrate an extrapolation procedure employed here, the critical compressibility factor *Z*c and the correlation function *C* at *T*c, for the neighboring spin pair are first treated in the case of two-dimensional square lattice. It turns out that the terms up to *w*8 for ln *Z* lead to the results within the error of 0.2 ~ 0.30% as compared to exact values. Along the same line, *Z*c and __C__ (average correlation function) are calculated for the Penrose lattice. The final results are *Z*c = 0. 138+-0.002 and __C__ = 0.673+-0.003.

### Keywords

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