Curie-Weiss Model under ℓ^p constraint and a Generalized Hubbard-Stratonovich Transform

2024/07/05 by Dey, Partha S., Kim, Daesung
#05C81 (Primary) #60F99 #60G50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.04875

Abstract

We consider the Ising Curie-Weiss model on the complete graph constrained under a given ℓ^p norm for some p>0. For p=∞, it reduces to the classical Ising Curie-Weiss model. We prove that for all p>2, there exists β_c(p) such that for β<β_c(p), the magnetization is concentrated at zero and satisfies an appropriate Gaussian CLT. In contrast, for β>β_c(p) the magnetization is concentrated at ± m_∗ for some m_∗>0. We have β_c(p)>1 for p>2 and lim_p→∞β_c(p)=3. We further generalize the model for general symmetric spin distributions and prove a similar phase transition. For 0

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