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Branched polymers and dimensional reduction. (English) Zbl 1140.82314

Summary: 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.

MSC:

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
60C05 Combinatorial probability
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C27 Dynamic critical phenomena in statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
82D60 Statistical mechanics of polymers
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