Dimensional Reduction Formulas for Branched Polymer Correlation Functions |
| |
Authors: | David C Brydges John Z Imbrie |
| |
Institution: | (1) Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road Vancouver, B.C., Canada, V6T 1Z2;(2) Department of Mathematics, University of Virginia, Charlottesville, Virginia, 22904-4137 |
| |
Abstract: | In BI01] 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
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. |
| |
Keywords: | Branched polymers Yang– Lee edge repulsive-core singularity dimensional reduction hard rods |
本文献已被 SpringerLink 等数据库收录! |
|