Temperature phase transitions associated with local minima of energy

We develop an alternative version of the theory of contour models adapted to continuous spins located in sites of a (d⩾2)-dimensional lattice. The spins interacting via nearest-neighbor ferromagnetic interactions are embedded in a single spin potential V similar to that already introduced by Dobrushin and Shlosman. The potential V has a finite-ordered sequence of local minima and satisfy certain conditions. For all finite-reciprocal temperatures less than one, we prove the Peierls condition and we show that there exists a sequence of first-order phase transition temperature points.