Finite-size effects in a dimer model of crystallization

A dimer model of two-dimensional crystallization in melts and solutions with strong interparticle correlations is proposed. The crystal phase is represented by a region of regularly packed vertical dimers growing from a selected layer in which the occupied and vacant vertical bonds alternate. The crystal growth may be stimulated by an “external staggered field” acting on the bonds in the selected layer. The difference of the average occupation numbers of odd and even bonds plays the role of an ordering parameter. In cases when the dimer ordering in the selected layer is imperfect, a coexistence of crystal domains with an orientationally disordered fluid phase takes place. For simplicity the lattice is taken in the form of an infinite cylinder and the dependence of the ordering parameter on the bond activities and finite-size effects with respect to one lattice dimension are studied rigorously. It is found that the ordering parameter vanishes in the thermodynamic limit for arbitrary finite values of the ordering field. The leading-order finite-size correction to the ordering parameter falls off with the increase of the finite lattice dimension L as L−1 for large L.