Journal of Statistical Physics, Vol. 72, Nos. 3/4, 1993. p. 737-772.
We present the thermodynamics of two variations of the interacting partially directed self-avoiding walk problem by discussing versions where the length of the walks assume real as well as a integral values. While the discrete model has been considered previously to varying degrees of success, the continuous model we now define has not. The examination of the continuous model leads to the exact derivation of several exponents. For the discrete model some of these exponents can be calculated using a continued-fraction representation...