Information-theoretic Analysis of Phase Transitions
Dirk V. Arnold
Department of Computer Science,
University of Dortmund, LS XI,
44221 Dortmund, Germany
Abstract
Despite using different formalizations and investigating very different kinds of systems, the same unimodal dependence between disorder and complexity has been found in several independently conducted studies. Maximally interesting behavior of complex systems was observed at "the edge of chaos,'' the onset of instability between the ordered and the chaotic regime. The particular shape of the complexity-disorder plot has led researchers to suggest that complex systems can have inherent nontrivial information processing capabilities in the vicinity of a phase transition. However, it has subsequently been pointed out that the observed kind of dependence is a consequence of the definition of disorder used in the studies and that a different definition would make the structure suggesting a phase transition vanish.
In this paper, the dependence between disorder and complexity for two-dimensional Ising spin systems is investigated. Measures not sharing the flaw pointed out above are used, and the hypothesis of maximally interesting behavior in the vicinity of a phase transition is confirmed for simple, spatially homogeneous systems with random noise. Moreover, evidence is presented that more complex systems in which frustration is present can show interesting behavior over a broad range of noise levels.
