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

Hiroki Ohta 1 Martin-Luc Rosinberg 2 Gilles Tarjus 2

Europhysics Letters, EDP Science, 2013, 104, pp.16003

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.

  • 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. LPTMC – Laboratoire de Physique Théorique de la Matière Condensée
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