支化聚合物关联函数的降维公式
Dimensional Reduction Formulas for Branched Polymer Correlation Functions
摘要：
在[math-ph/0107005]中，我们已经证明了D+2连续维中自避免支化聚合物的生成函数与D维中负活性的硬核连续气体的压力成比例。这一结果解释了为什么支化聚合物的临界行为应该与$i ϕ^3$（或杨-李边）场论（如Parisi和Sourlas在1981年提出的）在少两个维度上的临界行为相同。- 本文对文献[math-ph/0107005]的结果进行了回顾和推广。我们表明，几个支化聚合物的生成函数成正比的关联函数的硬核气体。我们推导出了某些支化聚合物关联式的沃德恒等式。给出了多组分支化聚合物和相应的排斥气体的约化公式。最后，我们推导出了一维硬核气体2点函数的质量标度极限，从而得到了三维支化聚合物2点函数的标度形式。
英文摘要：
In [math-ph/0107005] we have proven that the generating function for self-avoiding branched polymers in D+2 continuum dimensions is proportional to the pressure of the hard-core continuum gas at negative activity in D dimensions. This result explains why the critical behavior of branched polymers should be the same as that of the $i ϕ^3$ (or Yang-Lee edge) field theory in two fewer dimensions (as proposed by Parisi and Sourlas in 1981). - In this article we review and generalize the results of [math-ph/0107005]. We show that the generating functions for several branched polymers are proportional to correlation functions of the hard-core gas. We derive Ward identities for certain branched polymer correlations. We give reduction formulae for multi-species branched polymers and the corresponding repulsive gases. Finally, we derive the massive scaling limit for the 2-point function of the one-dimensional hard-core gas, and thereby obtain the scaling form of the 2-point function for branched polymers in three dimensions.
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