  We consider the $d=1$ Ising model with Kac potentials at inverse temperature
$\beta>1$ where mean field predicts a phase transition with two possible
equilibrium magnetization $\pm m_\beta$, $m_\beta>0$. We show that when the Kac
scaling parameter $\gamma$ is sufficiently small typical spin configurations
are described (via a coarse graining) by an infinite sequence of successive
plus and minus intervals where the empirical magnetization is "close" to
$m_\beta$ and respectively $-m_\beta$. We prove that the corresponding marginal
of the unique DLR measure is a renewal process.
