Interplay of surface preroughening, roughening, and melting in three dimensional lattice models

We elaborate upon a recently proposed surface model consisting of a domain wall induced by a twisted boundary condition in a three-dimensional N-state Potts model. The model is capable of describing simultaneously surface melting and roughening degrees of freedom and their interplay. The N different spin directions effectively describe the positional entropy, the location of the wall describes the height fluctuations, and both aspects coexist in the same system. Their interplay, known to give rise to an additional preroughening transition of the free-standing surface, is shown here to produce an adsorption phase diagram on an attractive substrate exhibiting the possibility of reentrant layering. The results provide a consistent scenario closely reminiscent of experimental results for multilayers of rare gases.