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Absence of site percolation at criticality in ℤ 2 × { 0 , 1 }
Author(s) -
Damron Michael,
Newman Charles M.,
Sidoravicius Vladas
Publication year - 2015
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20544
Subject(s) - percolation (cognitive psychology) , criticality , mathematics , directed percolation , extension (predicate logic) , boundary (topology) , graph , struct , statistical physics , combinatorics , discrete mathematics , critical exponent , phase transition , physics , condensed matter physics , computer science , mathematical analysis , neuroscience , nuclear physics , biology , programming language
In this note we consider site percolation on a two dimensional sandwich of thickness two, the graphℤ 2 × { 0 , 1 } . We prove that there is no percolation at the critical point. The same arguments are valid for a sandwich of thickness three with periodic boundary conditions. It remains an open problem to extend this result to other sandwiches. “Note added in proof: This extension has recently been accomplished in arXiv 1401.7130.” © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 328–340, 2015