15 citations · 36 across the 3 of their papers we have counts for
4 papers
Dimensional Reduction for Directed Branched Polymers
John Z. Imbrie
Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched…
Dimensional Reduction and Crossover to Mean-Field Behavior for Branched Polymers
John Z. Imbrie
This article will review recent results on dimensional reduction for branched polymers, and discuss implications for critical phenomena. Parisi and Sourlas argued in 1981 that bran…
End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions
David C. Brydges, John Z. Imbrie
In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Green's function for the process equals 1/x^2. If the process is mo…
Branched Polymers and Dimensional Reduction
David C. Brydges, John Z. Imbrie
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 c…