Renormalisation group approach to multifractal structure in random resistor networks just above the percolation threshold

Abstract

A renormalisation group method is presented to analyse the multifractal structure of the current distribution in random linear resistor networks just above the percolation threshold. The recursion relation for the current distribution is given under the renormalisation transformation. The distribution function of the current is derived with the use of the recursion relation. The fragmentation of the current is described as a random multiplicative process. An infinite set of exponents is calculated to scale each of the moments of the current distribution. The alpha -f spectrum is derived from the Legendre transform of these exponents. The authors' exponents, obtained by the relatively small-cell renormalisation, are very close to the previous simulation data.