ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Renormalization arguments are developed and applied to independent nearest-neighbor percolation on various subsets ℕ of ℤ d ,d≧2, yielding: Equality of the critical densities,p c (ℕ), for ℕ a half-space, quarter-space, etc., and (ford〉2) equality with the limit of slab critical densities. Continuity of the phase transition for the half-space, quarter-space, etc.; i.e., vanishing of the percolation probability,θ ℕ(p), atp=p c (ℕ). Corollaries of these results include uniqueness of the infinite cluster for such ℕ's and sufficiency of the following for proving continuity of the full-space phase transition: showing that percolation in the full-space at densityp implies percolation in the half-space at thesame density.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01321136
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