Abstract
We study the analyticity properties of the free energy f γ (m) of the Kac model at points of first order phase transition, in the van der Waals limit γ↘0. We show that there exists an inverse temperature β 0 and γ 0>0 such that for all β≥β 0 and for all γ∈(0,γ 0), f γ (m) has no analytic continuation along the path m↘m * (m * denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure p γ (h), which is related to the free energy f γ (m) by a Legendre transform.
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Friedli, S., Pfister, CE. Non-Analyticity and the van der Waals Limit. Journal of Statistical Physics 114, 665–734 (2004). https://doi.org/10.1023/B:JOSS.0000012506.98828.dd
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DOI: https://doi.org/10.1023/B:JOSS.0000012506.98828.dd