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arXiv · 1306.6368

Morphology transition at depinning in a solvable model of interface growth in a random medium

Hiroki Ohta·Martin-Luc Rosinberg·Gilles Tarjus
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Abstract

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 versus 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.

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Hiroki Ohta, Martin-Luc Rosinberg, Gilles Tarjus. 2013-06-26. Morphology transition at depinning in a solvable model of interface growth in a random medium. https://doi.org/10.1209/0295-5075%2F104%2F16003

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