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We study a heteropolymer model with random contact interactions introducedsome time ago as a simplified model for proteins. The model consists ofself-avoiding walks on the simple cubic lattice, with contact interactionsbetween nearest neighbor pairs. For each pair, the interaction energy is anindependent Gaussian variable with mean value $B$ and variance $\D^2$. For thismodel the annealed approximation is expected to become exact for low disorder,at sufficiently high dimension and in the thermodynamic limit. We show thatcorrections to the annealed approximation in the 3-d high temperature phase aresmall, but do not vanish in the thermodynamic limit, and are in good agreementwith our replica symmetric calculations. Such corrections derive from the factthat the overlap between two typical chains is nonzero. We explain why previousauthors had come to the opposite conclusion, and discuss consequences for thethermodynamics of the model. Numerical results were obtained by simulatingchains up to length 1400 by means of the recent PERM algorithm, in the coil andmolten globular phases, well above the freezing temperature.Comment: 20 pages, 9 figure

Exactness of the annealed and the replica symmetric approximations for random heteropolymers