Phase Transition on the Classical Dimer Model on a 3-4 Lattice

In this paper, we investigate if it occurs a phase transition for a system of classical dimers adsorbed on a 3-4 lattice in the thermodynamic limit. We define four types of bonds (denoted by the dimers activities adsorbed in her, $x$, $y$, $u$ and $v$) and evaluated the partition function from the combinatorial method of the pfaffian and using periodic boundary conditions. We write the density of free energy per particle and the condition to his analyticity, showing that there is a critical point for a determined choice of the activities. We also numerically evaluated the integral on free energy and their derivates (entropy and specific heat) for the same case and compute the entropy density and molecular freedom per particle at high temperatures for this choice of the activities.