Ground state of random copolymers and the discrete random energy model

We propose and investigate a modification of the random energy model where the energies of different states are still independent random values but may take only discrete values. This model appears naturally in studies of random heteropolymers with monomers of two types. We calculate the probability that the ground state of such a polymer is nondegenerate and test this result against a lattice model of a heteropolymer with exhaustively enumerated conformations. The theory is in excellent agreement with numerical experiment. Our results imply that the lower the energy of the ground state the less probable that it is degenerate. The probability of degeneracy decays exponentially as ground state energy decreases.