Branched Polymers and Dimensional Reduction
Mathematical Physics
2007-05-23 v2 Statistical Mechanics
math.MP
Abstract
We establish an exact relation between self-avoiding branched polymers in D+2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D+2 = 2,3,4 and show that they are corollaries of our result. We explain the connection (first proposed by Parisi and Sourlas) between branched polymers in D+2 dimensions and the Yang-Lee edge singularity in D dimensions.
Cite
@article{arxiv.math-ph/0107005,
title = {Branched Polymers and Dimensional Reduction},
author = {David C. Brydges and John Z. Imbrie},
journal= {arXiv preprint arXiv:math-ph/0107005},
year = {2007}
}
Comments
20 pages, 3 figures; v2: Green's function results added