EXACT ENUMERATION STUDY OF FREE-ENERGIES OF INTERACTING POLYGONS AND WALKS IN 2 DIMENSIONS

We present analyses of substantially extended series for both interact ing self-avoiding walks (ISAW) and polygons (ISAP) on the square latti ce. We argue that these provide good evidence that the free energies o f both linear and ring polymers are equal above the theta-temperature, thus extending the application of a theorem of Tesi et al to two dime nsions. Below the theta-temperature the conditions of this theorem bre ak down, in contradistinction to three dimensions, but an analysis of the ratio of the partition functions for ISAP and ISAW indicates that the free energies are in fact equal at all temperatures within 1% at l east. Any perceived difference can be interpreted as the difference in the size of corrections to scaling in both problems. This may be used to explain the vastly different values of the crossover exponent prev iously estimated for ISAP to thai predicted theoretically, and numeric ally confirmed, for ISAW. An analysis of newly extended neighbour-avoi ding self-avoiding walk series is also given.