Oriented polymers: A transfer matrix calculation

Based on transfer matrix techniques and finite-size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact values predicted recently. The polymer is also found to undergo a spiral transition for sufficiently strong attractive interaction. The fractal dimension of the polymer is computed in the repulsive and attractive regimes and at the spiral transition point. The later is found to be different from that at the collapse transition of the ordinary self-avoiding walk.