When does the chaos in the Curie-Weiss model stop to propagate? Article Swipe
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· 2023
· Open Access
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· DOI: https://doi.org/10.1214/23-ejp1039
· OA: W4388700366
We investigate increasing propagation of chaos for the mean-field Ising model of ferromagnetism (also known as the Curie-Weiss model) with N spins at inverse temperature β>0 and subject to an external magnetic field of strength h∈R. Using a different proof technique than in Ben Arous and Zeitouni [Ann. Inst. H. Poincaré: Probab. Statist., 35(1): 85–102, 1999] we confirm the well-known propagation of chaos phenomenon: If k=k(N)=o(N) as N→∞, then the k’th marginal distribution of the Gibbs measure converges to a product measure at β<1 or h≠0 and to a mixture of two product measures, if β>1 and h=0. More importantly, we also show that if k(N)∕N→α∈(0,1], this property is lost and we identify a non-zero limit of the total variation distance between the number of positive spins among any k-tuple and the corresponding binomial distribution.
