02-155 David C. Brydges and John Z. Imbrie
Dimensional Reduction Formulas for Branched Polymer Correlation Functions (44K, Latex with 1 ps figure) Mar 28, 02
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. In [BI01] (mp_arc:01-255) we have proven that the generating function for self-avoiding branched polymers in D+2 continuum dimensions is proportional to the pressure of the hard-core continuum gas at negative activity in D dimensions. This result explains why the critical behavior of branched polymers should be the same as that of the $i \phi^3$ (or Yang-Lee edge) field theory in two fewer dimensions (as proposed by Parisi and Sourlas in 1981). In this article we review and generalize the results of [BI01]. We show that the generating functions for several branched polymers are proportional to correlation functions of the hard-core gas. We derive Ward identities for certain branched polymer correlations. We give reduction formulae for multi-species branched polymers and the corresponding repulsive gases. Finally, we derive the massive scaling limit for the 2-point function of the one-dimensional hard-core gas, and thereby obtain the scaling form of the 2-point function for branched polymers in three dimensions.

Files: 02-155.src( 02-155.comments , 02-155.keywords , js.tex , graph5.eps )