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

TL;DR

This paper introduces an exactly solvable model of interface growth in a random medium, revealing a morphology transition at a multicritical point along the depinning transition line, with results comparable to numerical studies on cubic lattices.

Contribution

It presents a novel, exactly solvable model of interface depinning that captures the morphology transition and phase diagram similar to more complex numerical models.

Findings

Identifies a morphology transition at a multicritical point.

Shows the phase diagram matches numerical results on cubic lattices.

Provides exact asymptotic analysis of interface height and width.

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.