Explosive electric breakdown due to conducting-particle deposition on an insulating substrate.
We introduce a theoretical model to investigate the electric breakdown of a substrate on which highly conducting particles are adsorbed and desorbed with a probability that depends on the local electric field. We find that, by tuning the relative strength q of this dependence, the breakdown can change from continuous to explosive. Precisely, in the limit in which the adsorption probability is the same for any finite voltage drop, we can map our model exactly onto the q-state Potts model and thus the transition to a jump occurs at q = 4. In another limit, where the adsorption probability becomes independent of the local field strength, the traditional bond percolation model is recovered. Our model is thus an example of a possible experimental realization exhibiting a truly discontinuous percolation transition.
Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
Cláudio L N
CL
Oliveira
Computational Physics, IfB, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal and Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal.
Nuno A M
NA
Araújo
Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil and Computational Physics, IfB, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland.
José S
JS
Andrade
Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil and Computational Physics, IfB, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland.
Hans J
HJ
Herrmann