Aperiodicity and Disorder - Does it Matter?

Details Aperiodicity and Disorder - Does it Matter? Aperiodicity and Disorder - Does it Matter?

2000-10-25

arxiv.org/abs/cond-mat/0010392v1

published as "Aperiodicity and Disorder - Do They Play a Role?" in: Computational Statistical Physics: From Billiards to Monte

Physics

Condensed Matter

Statistical Mechanics

Contribution to the lecture notes of the Heraeus summer school on Statistical Physics, Chemnitz, September 2000 (will be publi

Scientific paper

The effects of an aperiodic order or a random disorder on phase transitions in statistical mechanics are discussed. A heuristic relevance criterion based on scaling arguments as well as specific results for Ising models with random disorder or certain kinds of aperiodic order are reviewed. In particular, this includes an exact real-space renormalization treatment of the Ising quantum chains with coupling constants modulated according to substitution sequences, related to a two-dimensional classical Ising model with layered disorder.

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