Spectral dimension and conductivity exponent of the percolating cluster

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Abstract
We discuss a recent conjecture by Alexander and Orbach about the spectral dimension d of a percolating cluster. We consider the transformation from percolation to backbone by removing the dangling ends, and those exponents which remain invariant in this transformation. We suggest d = (4( d + 2) - 4 η)/(3(d + 2) - 2 η) where d is the dimension of space, leading to the former conjecture if one supposes η = 0. This allows for an evaluation of the conductivity exponent t

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