## Random resistor network

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Taken from 0706.2968
The model of the random resistor network (RRN) is formulated on the square lattice with the lattice constant $a$ and sites labelled by integers $(i,j)$. Sites $(i,j)$, $(i^\prime ,j^\prime )$ with $|i'-i| > 1$, $|j'-j| > 1$ are not connected directly. Each pair of sites with $|i'-i|\leq 1$, and $|j'-j|\leq 1$, is connected by a link with the conductance ${\mathbb G}_{(i,j)}^{(i^\prime ,j^\prime )}\!\!={\mathbb G}_{(i^\prime ,j^\prime )}^{(i,j)}$
 (1) (2) (3)
Here $\eta _{i,j}$ is a random variable,
 (4)
where $\langle \dots \rangle$ means the ensemble averaging.