On the Thermodynamic Limit in Random Resistors Networks

Details On the Thermodynamic Limit in Random Resistors Networks On the Thermodynamic Limit in Random Resistors Networks

1996-05-21

arxiv.org/abs/cond-mat/9605132v2

Physics

Condensed Matter

14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics A

Scientific paper

10.1088/0305-4470/29/22/023

We study a random resistors network model on a euclidean geometry $\bt{Z}^d$. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.

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