Phase diagram of random heteropolymers

We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered.