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- W2156578204 abstract "This article will review recent results on dimensional reduction for branched polymers, and discuss implications for critical phenomena. Parisi and Sourlas argued in[PS81]that branched polymers fall into the universality class of the Yang-Lee edge in two fewer dimensions. Brydges and I have proven in[BI01]that the generating function for self-avoiding branched polymers inD +2 continuum dimensions is proportional to the pressure of the hard-core continuum gas at negative activity inDdimensions (which is in the Yang-Lee ori (phi ^3 ) class). I will describe how this equivalence arises from an underlying supersymmetry of the branched polymer model.I will also use dimensional reduction to analyze the crossover of two-dimensional branched polymers to their mean-field limit, and to show that the scaling is given by an Airy function (the same as in[Car01]).KeywordsDimensional ReductionCritical ExponentUniversality ClassAiry FunctionNegative ActivityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W2156578204 created "2016-06-24" @default.
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- W2156578204 date "2003-01-01" @default.
- W2156578204 modified "2023-10-16" @default.
- W2156578204 title "Dimensional Reduction and Crossover to Mean-Field Behavior for Branched Polymers" @default.
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- W2156578204 doi "https://doi.org/10.1007/978-3-0348-7907-1_35" @default.
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