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Mean field replica theory is employed to analyze the freezing transition ofrandom heteropolymers comprised of an arbitrary number ($q$) of types ofmonomers. Our formalism assumes that interactions are short range andheterogeneity comes only from pairwise interactions, which are defined by anarbitrary $q \times q$ matrix. We show that, in general, there exists afreezing transition from a random globule, in which the thermodynamicequilibrium is comprised of an essentially infinite number polymerconformations, to a frozen globule, in which equilibrium ensemble is dominatedby one or very few conformations. We also examine some special cases ofinteraction matrices to analyze the relationship between the freezingtransition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur

Freezing transition of random heteropolymers consisting of an arbitrary set of monomers