Polymerization in a ferromagnetic spin model with threshold

We propose a spin model with a new kind of ferromagnetic interaction, which may be called ferromagnetic coupling with threshold. In this model the contribution of a given spin to the total energy has only two possible values and depends on the number of parallel spins among its nearest and next to nearest neighbors. By mapping the model onto the Ising version of the isotropic eight-vertex model, we obtain some evidence of a low temperature phase made of alternate parallel plus and minus polymers, in which the spin is aligned with the majority of its neighbors.