A directed self-avoiding walk model is solved exactly for a finite cylinder geometry where the cylinder's axis is parallel to the directed axis of the walk. The finite-size scaling behavior of the longitudinal and transverse correlation lengths is examined. Although the infinite system has a continuous transition, one of the scaling variables for the finite system varies exponentially with the cylinder circumference, which is reminiscent of finite-size effects at first-order transitions in scalar-spin systems.

• Received 1 August 1983

DOI:https://doi.org/10.1103/PhysRevB.28.6613