From collapse to freezing in random heteropolymers

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N-H (out of N) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho(H) = N-H/N. The average chain size scales as R similar or equal to (NF)-F-1/d(rho(H)) (d is the space dimension). As rho(H) --> 0, F(rho(H)) similar to rho(H)(zeta) with zeta = 1/d - nu = -1/4 for d = 2. Moreover, for 0 < rho(H) < 1, entropy per monomer approaches zero as N --> infinity (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R similar to N-nu) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.