Physics – Condensed Matter
Scientific paper
1996-04-15
Nuclear Physics B 490 (1997) 511-542
Physics
Condensed Matter
28 pages, revtex, 4 Postscript figures, 3 latex emlines pictures. Replacement eliminates conflict with a blob result
Scientific paper
10.1016/S0550-3213(97)00096-5
We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show factorization of its partition sum by a short chain factor and a long chain factor in the short chain limit. This corresponds to an expansion for short distance along the fractal perimeter of the polymer chains connecting the vertices and is related to a large mass expansion of field theory. The scaling of the second virial coefficient for bimodal solutions is explained. Our method also applies to the correlations of the multifractal measure of harmonic diffusion onto an absorbing polymer. We give a result for expanding these correlations for short distance along the fractal carrier of the measure.
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