  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.
