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

Author： Ohta Hiroki Rosinberg Martin Luc Tarjus Gilles

E-ISSN： 1286-4854|104|1|16003-16003

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.104, Iss.1, 2013-11, pp. : 16003-16003

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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 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.