Abstract
We consider bond percolation on \({\mathbb {Z}}^d\times {\mathbb {Z}}^s\) where edges of \({\mathbb {Z}}^d\) are open with probability \(p<p_c({\mathbb {Z}}^d)\) and edges of \({\mathbb {Z}}^s\) 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 \(p_c({\mathbb {Z}}^d)\). The results are related to the so-called dimensional crossover from \({\mathbb {Z}}^d\) to \({\mathbb {Z}}^{d+s}\).
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05 June 2018
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Acknowledgements
Rémy Sanchis was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Grant PPM 00600/16. Roger W. C. Silva was partially supported by FAPEMIG, Grant APQ-02743-14. We would like to thank Cristiano Santos Benjamin for his help with Fig. 1, John William MacQuarrie, who carefully read the manuscript, and Sacha Friedli for helpful discussions.
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Sanchis, R., Silva, R.W.C. Dimensional Crossover in Anisotropic Percolation on \({\mathbb {Z}}^{d+s}\) . J Stat Phys 169, 981–988 (2017). https://doi.org/10.1007/s10955-017-1905-9
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DOI: https://doi.org/10.1007/s10955-017-1905-9