Dimensional Crossover in Anisotropic Percolation on Zd+s

We consider bond percolation on Z d × Z s where edges of Z d are open with probability p < p c ( Z d ) and edges of Z s are open with probability q , independently of all others. We obtain bounds for the critical curve in ( p ,  q ), with p close to the critical threshold p c ( Z d ) . The result...

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Bibliographic Details
Published in:Journal of statistical physics 2017, Vol.169 (5), p.981-988
Main Authors: Sanchis, Rémy, Silva, Roger W. C.
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We consider bond percolation on Z d × Z s where edges of Z d are open with probability p < p c ( Z d ) and edges of Z s are open with probability q , independently of all others. We obtain bounds for the critical curve in ( p ,  q ), with p close to the critical threshold p c ( Z d ) . The results are related to the so-called dimensional crossover from Z d to Z d + s .
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1905-9