2006/02/20 by Aernout C. D. van Enter, A. C. D. van Enter, Christof Külske +1 · 15 citations
Mathematics · Physics and Astronomy · #Artificial intelligence #Complex system #Computer science #Condensed matter physics #Field (mathematics) #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Materials science #Mathematical analysis #Mathematics #Mean field theory #Physics #Property (philosophy) #Pure mathematics #Range (aeronautics) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Variety (cybernetics) #math-ph #math.MP #math.PR
paper · pdf · doi:10.1007/s10955-006-9185-9
published in Journal of Statistical Physics 126(4-5), 1007-1024 (Springer Science+Business Media)
arxiv created 2006/02/20 · openalex publication_date 2006/08/07 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) From disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical interest. 2) Of disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems. We discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field non-Gibbsian properties.