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This ultimately relates to a physics question, but It wasn't getting any answers, on physics.stackexchange. As it crosses the boundaries of each subject I was advised to post it here:

Has a system where conducting sites can percolate by hopping over/tunnelling through a non-conducting site been described? If so what are the characteristics, and where can I find more details (such as a paper on the subject)?

In the image below, if the edge of a black square touches the edge of another black it 'conducts' across. That could be described as singularly percolated.

I'm trying to describe a system whereby the 'conduction' can hop over a white square.

Does this have a name? Is it formally described in a paper anywhere?

Percolation grid

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    @did... I'll see if I remember when I get home2014-04-02

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Yes it's called variable range hoping. You can find papers by Faggionato, Mathieu on arxiv.

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    Hi Antoine. As your answer stands, it is very minimal. It might be helpful to future viewers if you were to expand your answer with more context and details--perhaps linking to specific papers which address the OP's question2018-01-17