2-STAGE COLLAPSE OF A POLYMER-CHAIN IN 2 DIMENSIONS

I show that for a certain range in its parameter space, a self-attracting self-avoiding loop (SASAL) can be mapped onto the bull of a percolation cluster in two dimensions. The inside (outside) of this loop attracts itself with interaction energy epsilon(+) (epsilon(-)). This mapping is used to argue that if epsilon(+)>epsilon(-), the collapse of the SASAL occurs in not one but two stages as the temperature is reduced: the SASAL first collapses to form a ''branched polymer'' and then at lower temperatures collapses still further to become a compact globule.