  Mean field replica theory is employed to analyze the freezing transition of
random heteropolymers comprised of an arbitrary number ($q$) of types of
monomers. Our formalism assumes that interactions are short range and
heterogeneity comes only from pairwise interactions, which are defined by an
arbitrary $q \times q$ matrix. We show that, in general, there exists a
freezing transition from a random globule, in which the thermodynamic
equilibrium is comprised of an essentially infinite number polymer
conformations, to a frozen globule, in which equilibrium ensemble is dominated
by one or very few conformations. We also examine some special cases of
interaction matrices to analyze the relationship between the freezing
transition and the nature of interactions involved.
