Kd. Machado et Jf. Stilck, STUDY OF POLYMERS WITH CROSSING BONDS ON THE SQUARE LATTICE, Journal of physics. A, mathematical and general, 30(5), 1997, pp. 1445-1455
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.