Field-theoretic formalism for several polymers

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Abstract
De Gennes' proposal (see J. Physique Lett., vol.36, p.55 (1975)) that the n to 0 limit of an O(n) symmetric theta 4 theory describes a single polymer chain in solution is extended to allow for the interactions between several polymer chains. To describe m interacting polymers, it is found to be necessary to employ an (m*n)-component field theory before taking the n to 0 limit. Explicit calculation of the second virial coefficient of the osmotic pressure for self-avoiding walks on a Bethe lattice is performed to illustrate the formalism.