Thermodynamic behavior of a polymer with interacting bonds on a square lattice

Using the transfer matrix technique, finite-size scaling, phenomenological renormalization group, and conformal invariance ideas, the thermodynamic behavior of a polymer with interacting bonds on a square lattice has been studied. In this model, one monomer that belongs to the polymer has an activity x=e^βμ, while the interactions between bonds of the polymer that are located on opposite edges of elementary squares of the lattice have a statistical weight y=e^-βε, where ε is the interaction energy. Next, the phase diagram of the model in the (x,y) plane was found, which shows three phases, two of them being polymerized. Furthermore, the densities of occupied sites and of bond interactions in each phase were calculated, in order to determine the nature of the transitions between the phases. The results obtained are consistent with a second-order transition line between the nonpolymerized and the regular polymerized phase and a first-order transition between the nonpolymerized and the dense polymerized phase. The boundary between both polymerized phases may be of first or second order, and thus evidence for a tricritical point is found.