2010/10/31 by Alain Billoire, Imre Kondor, Jovanka Lukic +1
Economics, Econometrics and Finance · Materials Science · Physics and Astronomy · #Character (mathematics) #Complex Systems and Time Series Analysis #Distribution (mathematics) #Material Dynamics and Properties #Mean field theory #Phase (matter) #Random field #Range (aeronautics) #Space (punctuation) #Spin glass #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1088/1742-5468/2011/02/p02009
published as J. Stat. Mech. (2011) P02009 · Added a few references and a comment phrase
arxiv created 2010/11/02 · openalex publication_date 2011/02/01 · arxiv updated 2011/02/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range character of correlations is translated into a broad distribution of the spin–spin correlation coefficients for almost all realizations of the random couplings. When we sample the whole phase space we find that this distribution is indeed so broad that at low temperatures it essentially becomes uniform, with all possible correlation values appearing with the same probability. The distribution of correlations inside a single phase space valley is also studied and found to be much narrower.