Morphology transition at depinning in a solvable model of interface growth in a random medium
1 LPTMS, CNRS-UMR 8626 and Université Paris-Sud - 91405 Orsay Cedex, France
2 LPTMC, CNRS-UMR 7600, Université Pierre et Marie Curie - 4 place Jussieu, Paris Cedex 05, France
Received: 27 June 2013
Accepted: 2 October 2013
We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field vs. disorder strength) qualitatively similar to that obtained numerically on the cubic lattice. We then introduce a specifically tailored random graph that allows an exact asymptotic analysis of the height and width of the interface. We characterize the change of morphology of the interface as a function of the disorder strength, a change that is found to take place at a multicritical point along the depinning-transition line.
PACS: 68.35.Ct – Interface structure and roughness / 75.10.Nr – Spin-glass and other random models / 75.78.Fg – Dynamics of domain structures
© EPLA, 2013