Partition function zeros of aperiodic Ising models

Details Partition function zeros of aperiodic Ising models Partition function zeros of aperiodic Ising models

2001-10-24

arxiv.org/abs/cond-mat/0110520v1

Quantum Theory and Symmetries, edited by E. Kapuscik and A. Horzela (World Scientific, Singapore, 2002) pp. 354-359

Physics

Condensed Matter

Statistical Mechanics

Invited talk at QTS2, Krakow, July 2001; 6 pages, several postscript figures, World Scientific proceedings LaTeX style

Scientific paper

We consider Ising models defined on periodic approximants of aperiodic graphs. The model contains only a single coupling constant and no magnetic field, so the aperiodicity is entirely given by the different local environments of neighbours in the aperiodic graph. In this case, the partition function zeros in the temperature variable, also known as the Fisher zeros, can be calculated by diagonalisation of finite matrices. We present the partition function zero patterns for periodic approximants of the Penrose and the Ammann-Beenker tiling, and derive precise estimates of the critical temperatures.

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