The freezing transition as a symmetry breaking phenomenon

A model for the freezing transition where a crystalline seed induces symmetry breakage is discussed. The seed is an array of sticky sites and we have analyzed the case of vanishing sticky potential. We consider a two-dimensional lattice and show that, within the framework of the Yang and Lee theory of phase transitions, the excess free energy of the system is a many valued function of the fugacity. In our simple model one of the branches corresponds to the liquid phase and the other to the solid state. We take first the infinite size limit and then the vanishing sticky limit. We have performed Monte Carlo simulations that indicate clearly that these limits do not commute