On the concept of long range order in solids: the use of algorithmic complexity

摘要

The paper focus on the ongoing discussion on how to better define the notion of crystallinity. We suggest that the use of algorithmic complexity captures, from a mathematical point of view, the notion of long range order in solids without the need of referring to the nature of the diffraction pattern. The possibility to compare different degrees of "crystallinity" by means of the corresponding algorithmic complexity is discussed. The diffraction space is studied from the same perspective., and it is proven that zero algorithmic complexity of the diffraction pattern does not imply the same result for the arrangement of atoms.