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We provide the exact generating function for semi-flexible and super-flexibleinteracting partially directed walks and also analyse the solution in detail.We demonstrate that while fully flexible walks have a collapse transition thatis second order and obeys tricritical scaling, once positive stiffness isintroduced the collapse transition becomes first order. This confirms a recentconjecture based on numerical results. We note that the addition of anhorizontal force in either case does not affect the order of the transition. Inthe opposite case where stiffness is discouraged by the energy potentialintroduced, which we denote the super-flexible case, the transition alsochanges, though more subtly, with the crossover exponent remaining unmoved fromthe neutral case but the entropic exponents changing.

Exact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed Walks