Lee-Yang zeros for substitutional systems

Details Lee-Yang zeros for substitutional systems Lee-Yang zeros for substitutional systems

1999-02-03

arxiv.org/abs/cond-mat/9902052v1

Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri, World Scientific, Singapo

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

Qualitative and quantitative information about critical phenomena is provided by the distribution of zeros of the partition function in the complex plane. We apply this idea to Ising models on non-periodic systems based on substitution. In 1D we consider the Thue-Morse chain and show that the magnetic field zeros are filling a Cantor subset of the unit circle, the gaps being related to a general gap labeling theorem. In 2D we study the temperature zeros of the Ising model on the Ammann-Beenker tiling. The use of corner transfer matrices allows an efficient calculation of the partition function for rather large patches which results in a reasonable estimate of the critical temperature.

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