From collapse to freezing in random heteropolymers

We consider a two-letter self-avoiding (square) lattice heteropolymer model of NH (out of N) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction ρH = NH/N. The average chain size scales as R N1/dF(ρH) (d is the space dimension). As ρH → 0, F(ρH) ~ ρHζ with ζ = 1/d − ν = − 1/4 for d = 2. Moreover, for 0 < ρH < 1, entropy per monomer approaches zero as N → ∞ (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R ~ Nν) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.