STUDY OF POLYMERS WITH CROSSING BONDS ON THE SQUARE LATTICE

Using the transfer matrix technique, finite-size scaling, phenomenolog ical renormalization group and conformal invariance ideas, we studied the model of polymers with crossing bonds on the square lattice. We de fine an activity x = e(-beta mu) for bonds and an activity y = e(-beta epsilon)e(-2 beta mu) for a crossing of two bonds, where epsilon is t he interaction energy between the two bonds. We calculated the correla tion length for two strips of widths L and L' and we found the fixed p oints of the phenomenological renormalization group equations. Within this formalism, we obtained the phase diagram for this model which sho ws three phases, two of them being polymerized. The estimated values o f the exponents nu and eta along the transition between the non-polyme rized phase and regular polymerized phase are consistent with nu = 3/4 and eta = 5/24, believed to be exact for y = 0.