Abstract
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 theexact derivation of several exponents. For the discrete model some of these exponents can be calculated using a continued-fraction representation. For both models the crossover exponentφ is found to be 2/3. Moreover, we confirm the tricritical nature of the collapse transition in the generalized ensemble and calculate the full scaling form of the generating function. Additionally, the similarities noticed previously to other models, but left unexplored, are explained with the aid of necklacing arguments.
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Owczarek, A.L., Prellberg, T. & Brak, R. The tricritical behavior of self-interacting partially directed walks. J Stat Phys 72, 737–772 (1993). https://doi.org/10.1007/BF01048031
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DOI: https://doi.org/10.1007/BF01048031