2023/07/11 by Jalowy, Jonas, Kabluchko, Zakhar, Löwe, Matthias +1
#60F05 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 82B05 #Probability (math.PR) #Secondary: 82B20
paper · doi:10.48550/arxiv.2307.05335
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, Zeitouni; 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.