Branched polymers and dimensional reduction
نویسندگان
چکیده
منابع مشابه
Branched Polymers and Dimensional Reduction
We establish an exact isomorphism between self-avoiding branched polymers in D + 2 continuum dimensions and the hard-core continuum gas at negative activity. 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 an...
متن کاملLecture on Branched Polymers and Dimensional Reduction
This is a pedagogical account of the some of the recent results of Brydges and Imbrie, described from the point of view of Grassmann integration. Some simple extensions are pointed out. Historical Introduction The subject of dimensional reduction, in the context considered in this lecture, has a long and rather peculiar history. The strangest aspect of all is that the simplest formulation of th...
متن کاملDimensional Reduction for Directed Branched Polymers
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 polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: γ(D + 1) = α(D)...
متن کاملDimensional Reduction and Crossover to Mean-Field Behavior for Branched Polymers
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 in D + 2 continuum di...
متن کاملBranched Polymers
Intended as models in chemistry or biology, branched polymers are often modeled, in turn, by lattice animals (trees on a grid); see, e.g., [3, 5, 8, 10, 18, 19]. However, continuum polymers turn out to be in some respects more tractable than their grid cousins. In order to study the behavior of branched polymers, and in particular to define and understand what random examples look like, we must...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2003
ISSN: 0003-486X
DOI: 10.4007/annals.2003.158.1019