THE TRICRITICAL BEHAVIOR OF SELF-INTERACTING PARTIALLY DIRECTED WALKS

We present the thermodynamics of two variations of the interacting par tially directed self-avoiding walk problem by discussing versions wher e the length of the walks assume real as well as a integral values. Wh ile the discrete model has been considered previously to varying degre es of success, the continuous model we now define has not. The examina tion of the continuous model leads to the exact derivation of several exponents. For the discrete model some of these exponents can be calcu lated using a continued-fraction representation. For both models the c rossover exponent phi is found to be 2/3. Moreover, we confirm the tri critical nature of the collapse transition in the generalized ensemble and calculate the full scaling form of the generating function. Addit ionally, the similarities noticed previously to other models, but left unexplored, are explained with the aid of necklacing arguments.