On the thermodynamic limit in random resistors networks

DOI10.1088/0305-4470/29/22/023zbMATH Open0905.60084arXivcond-mat/9605132OpenAlexW2156854605MaRDI QIDQ4393771

M. Talevi, Francesco Guerra

Publication date: 19 January 1999

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: We study a random resistors network model on a euclidean geometry $$. 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.

Full work available at URL: https://arxiv.org/abs/cond-mat/9605132

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

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