A note on the dimensional crossover critical exponent

Author(s)

Gomes, Pablo A. ^[1] ; Sanchis, Remy ^[1] ; Silva, Roger W. C. ^[2]

Affiliation

^[1] Univ Fed Minas Gerais, Dept Matemat, Belo Horizonte, MG - Brazil

^[2] Univ Fed Minas Gerais, Dept Estat, Belo Horizonte, MG - Brazil

• Document type: Journal article
• Source: LETTERS IN MATHEMATICAL PHYSICS; v. 110, n. 12 NOV 2020.
• Web of Science Citations: 0

Abstract

We consider independent anisotropic bond percolation on Z(d) x Z(s) where edges parallel to Zd are open with probability p < p(c)(Z(d)) and edges parallel to Z(s) are open with probability q, independently of all others. We prove that percolation occurs for q >= 8d(2)(p(c)(Z(d)) - p). This fact implies that the so-called Dimensional Crossover critical exponent, if it exists, is greater or equal than 1. In particular, using known results, we conclude the proof that, for d >= 11, the crossover critical exponent exists and equals 1. (AU)

• FAPESP's process: 20/02636-3 - Stochastic models on random environments
• Grantee: Pablo Almeida Gomes
• Support Opportunities: Scholarships in Brazil - Post-Doctoral