Year: 1999
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Simon, Harald, Baake, Michael, Grimm, Uwe
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1914408159