## The Annals of Probability

### An Upper Bound on the Critical Percolation Probability for the Three- Dimensional Cubic Lattice

#### Abstract

We prove that the critical probability for site percolation on the three-dimensional cubic lattice satisfies the inequality $p^{(3)}_c < 1/2$. An application to the three-dimensional Ising model is given.

#### Article information

Source
Ann. Probab., Volume 13, Number 2 (1985), 478-491.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993004

Digital Object Identifier
doi:10.1214/aop/1176993004

Mathematical Reviews number (MathSciNet)
MR781418

Zentralblatt MATH identifier
0567.60096

JSTOR