The Annals of Probability

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

M. Campanino and L. Russo

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82A67

Keywords
Graph Bernoulli measure chain cluster critical percolation probability pivotal sites Ising model

Citation

Campanino, M.; Russo, L. An Upper Bound on the Critical Percolation Probability for the Three- Dimensional Cubic Lattice. Ann. Probab. 13 (1985), no. 2, 478--491. doi:10.1214/aop/1176993004. https://projecteuclid.org/euclid.aop/1176993004


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