  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, attractive regimes and
at the spiral transition point. The later is found to be different from that at
the collapse transition of ordinary self-avoiding walk.
