2001/07/31 by David C. Brydges, John Z. Imbrie · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.MP #msc:82B41 #msc:82B27 #msc:82B21
published as Annals of Mathematics 158, 1019-1039 (2003) · 20 pages, 3 figures; v2: Green's function results added
arxiv created 2002/01/15 · arxiv updated 2009/11/30
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.