We consider a class of classical lattice spin systems, with $\mathbb{R}^n$-valued spins and two-body interactions. Our main result states that the associated Gibbs measure localizes in certain cylindrical neighbourhoods of the global minima of the unperturbed Hamiltonian. As an application we establish existence of a first order phase transition at low temperature, for a reflection positive mexican hat model on $\mathbb{Z}^d$, $d\geq 3$, with a non-ferromagnetic interaction.