We solve models for self-avoiding walks on Husimi lattices of coordination number $q=2\mathrm{}(\sigma +1\mathrm{}),\sigma =1,2,\dots$ made up of squares. An attractive interaction is introduced between first-neighbor sites incorporated into the walk or between bonds on opposite edges of elementary squares. For $\sigma >1\mathrm{}$ one polymerized phase is present in the phase diagram and the $\Theta$ point is a tricritical point. For $\sigma =1\mathrm{}$, however, two distinct polymerized phases appear, and the $\Theta$ point is a tricritical point (attractive sites) or a critical end point (attractive bonds).

• Received 3 November 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.2734