Non-Analyticity and the van der Waals Limit

Details Non-Analyticity and the van der Waals Limit Non-Analyticity and the van der Waals Limit

2003-02-24

arxiv.org/abs/cond-mat/0302480v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1023/B:JOSS.0000012506.98828.

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 Legendre transform.

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