Phase diagram of random heteropolymers: Replica approach and application of a new Monte Carlo algorithm.

In this contribution we present a study of the phase diagram of the Random Bond Heteropolymer model, introduced in 1988 as a simplified model for Prot ein Folding. In its lattice version, only non-bonded monomers on neighborin g sites interact. The interactions at each pair of neighbors are independen t Gaussian variables. Two phase transitions are expected: the usual collapse transition and a fre ezing transition after which only a finite number of different contact maps are relevant. The two transition Lines cross at a triple point. For larger disorder, the collapse happens inside the frozen phase. In the frozen phas e the entropy of the set of contact maps is non-extensive, and the specific entropy of the system is dominated by the configurational entropy at the c ontact maps kept fixed. At low density this is finite. At very high density contact maps determine their configuration, and the entropy is zero. Thus we conjecture the existence of a new phase transition where the latter entr opy vanishes. In the phase with zero entropy the freezing is abrupt: the gr ound state structures are the relevant ones at freezing and remain stable a s temperature is lowered. In the other phase the freezing is gradual and th e ground state structures are stable only at zero temperature. But we canno t exclude that abrupt freezing takes place only for maximally compact struc tures, thus only in the limit in which all interactions are attractive and T --> 0. Simulations confirm fully some features of this picture (for instance, the collapse transition before the freezing seems is very well predicted by the annealed approximation), while not much can be said about the existence of the conjectured phase transition. The Monte Carlo method that we used, the Pruned Enriched Rosenbluth Method (PERM), has proved to be very efficient. Its principles and its implementat ion are described in an Appendix. (C) 2000 Elsevier Science B.V. All rights reserved.