ISSN:
1572-9613
Keywords:
Percolation
;
critical exponent for percolation probability
;
percolation in sectors
;
strict inequalities
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponentβ for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL(ϕ):={(x, y):x=r cosθ, y=r sinθ for some r⩾0, orθ⩽ϕ} andβ(ϕ):=limp↓p c [log(p−p c )]−1 log Pcr {itO is connected to ∞ by an occupied path inL(ϕ)}, thenβ(ϕ) is strictly decreasing inϕ on [0, 2π]. Similarly, limn→∞ [−logn]−1 logP cr {itO is connected by an occupied path inL(ϕ)(ϕ) to the exterior of [−n, n]×[−n, n] is strictly decreasing inϕ on [0, 2π].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01011155
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