Absence of singular continuous diffraction for discrete multi-component particle models

Details Absence of singular continuous diffraction for discrete multi-component particle models Absence of singular continuous diffraction for discrete multi-component particle models

2007-09-13

arxiv.org/abs/0709.2061v2

J. Stat. Phys. 130 (2008) 727-740

Physics

Mathematical Physics

14 pages; revised version with minor improvements and updates

Scientific paper

10.1007/s10955-007-9445-3

Particle models with finitely many types of particles are considered, both on $\mathbb{Z}^d$ and on discrete point sets of finite local complexity. Such sets include many standard examples of aperiodic order such as model sets or certain substitution systems. The particle gas is defined by an interaction potential and a corresponding Gibbs measure. Under some reasonable conditions on the underlying point set and the potential, we show that the corresponding diffraction measure almost surely exists and consists of a pure point part and an absolutely continuous part with continuous density. In particular, no singular continuous part is present.

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