Modelos de dímeros em redes planares mistas

Abstract

In this study we present solutions for dimer models in mixed planar lattices, obtained from combinatorial method. In this method the partition function is obtained from the pfaffian associated with the problem. Particularly, in the thermodynamic limit, the free energy densities for 4-6, 3-6 and 3-4 lattices were determined. Besides the determination of the free energy for each case, we also computed the molecular freedom and the density of entropy in the high temperature limit. We considered three types of distinct 4-6 lattices, in which two of them exhibit phase transition. We also discuss the solutions for two types of 3-6 lattices which exhibit critical behavior similar to the 4-6 lattices cases discussed in the present work. The 3-4 lattice is geometrically similar to the triangular lattice problem, but presents distinct critical behavior. In all cases, we study numerically the behavior of free energy density as well as the behavior of its first derivatives, in order to better understand the thermodynamic behavior of the corresponding system. We also revise some results already presented in literature for the square, hexagonal, triangular and the mixed 4-8 lattices, treated by the pfaffian combinatorial approach.