Branched Polymers and Dimensional Reduction

Details Branched Polymers and Dimensional Reduction Branched Polymers and Dimensional Reduction

2001-07-08

arxiv.org/abs/math-ph/0107005v2

Annals of Mathematics 158, 1019-1039 (2003)

Physics

Mathematical Physics

20 pages, 3 figures; v2: Green's function results added

Scientific paper

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.

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