Correlation Length and its Critical Exponents for Percolation Processes.
Abstract
This document first defines the model and introduce the notation the author uses in this paper. A site percolation process in Z sub d (here d > or = 2) is a family of probability measures P sub p, P epsilon (0, 1) together with a collection of random variables eta: : Z sub d approx (0,1) such that under P sub p the eta's are independent and P sub p (eta)(x) = 1 = p. A site x is thought of being occupied (nonoccupied) if eta(x) = 1 (eta(x) = 0). We say that x is connected to y if there is a path of occupied sites connecting x and y; i.e. there is a sequence of sites x sub 0 =x, x sub 1, x sub 2,..., x sub n = y in Z sub d so that x sub i and x sub i + 2 are nearest neighbors and eta(x sub i) = 1 for every i = 0,1,2..., n. We denote this event by (x approaches limit of y). Let C sub O = ( a : 0 approaches limit of x). We say that C sub O is the cluster containing O.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1986
- Accession Number
- ADA174860
Entities
People
- B. G. Nguyen
Organizations
- University of North Carolina at Chapel Hill