- 03-72 Friedli S., Pfister C.-E.
- Non-Analyticity and the van der Waals Limit
Feb 24, 03
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Abstract. We study the analyticity properties of the free energy $f_\ga(m)$
of the Kac model at points of first order phase transition,
in the van der Waals limit $\ga\searrow 0$.
We show that there exists an inverse temperature
$\beta_0$ and $\ga_0>0$ such that for all $\beta\geq
\beta_0$ and for all $\ga\in(0,\ga_0)$,
$f_\ga(m)$ has no analytic continuation along the path $m\searrow m^*$
($m^*$ denotes spontaneous magnetization).
The proof consists in studying high order derivatives of the pressure
$p_\ga(h)$, which is related to the free energy $f_\ga(m)$ by a