Dimensional Reduction Formulas for Branched Polymer Correlation Functions

Abstract

In [math-ph/0107005] 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 $i{\varphi }^3$ (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 [math-ph/0107005]. 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.

14 pages, 2 figures, v2: references, typos

References in corpus (1)

• Identity of the universal repulsive-core singularity with Yang-Lee edge criticality

Cited by in corpus (4)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Dimensional Reduction and Crossover to Mean-Field Behavior for Branched Polymers
• Lecture on Branched Polymers and Dimensional Reduction
• Dimensional reduction for generalized continuum polymers