  In this paper we prove the existence of phase transitions at finite
temperature for O(n) classical ferromagnetic spin models on infrared finite
graphs. Infrared finite graphs are infinite graphs with $\lim {m\to 0^+} {\bar
Tr (L+m)^{-1} < \infty$, where $L$ is the Laplacian operator of the graph. The
ferromagnetic couplings are only requested to be bounded by two positive
constants. The proof, inspired by the classical result of Fr\"ohlich, Simon and
Spencer on lattices, is given through a rigorous bound on the average
magnetization. The result holds for $n\ge 1$ and it includes as a particular
case the Ising model.
