  Let $A$ be a finite set and $\phi:A^Z\to R$ be a locally constant potential.
For each $\beta>0$ ("inverse temperature"), there is a unique Gibbs measure
$\mu_{\beta\phi}$. We prove that, as $\beta\to+\infty$, the family
$(\mu_{\beta\phi})_{\beta>0}$ converges (in weak-$^*$ topology) to a measure we
characterize. It is concentrated on a certain subshift of finite type which is
a finite union of transitive subshifts of finite type. The two main tools are
an approximation by periodic orbits and the Perron-Frobenius Theorem for
matrices \'a la Birkhoff. The crucial idea we bring is a "renormalization"
procedure which explains convergence and provides a recursive algorithm to
compute the weights of the ergodic decomposition of the limit.
