Spherical model of growing interfaces

TL;DR

The paper introduces the Arcetri model, an exactly solvable model for growing interfaces, revealing universal properties and connections to spin glasses and reaction models across different dimensions.

Contribution

It presents the Arcetri model, a new exactly solvable framework for growing interfaces, highlighting its universal features and relations to other physical models.

Findings

Universal characteristics distinguish the Arcetri model from the Edwards-Wilkinson model for all dimensions except 2.

For d=1, the model is equivalent to the p=2 spherical spin glass.

In 2<d<4, its relaxation properties relate to a bosonic reaction model.

Abstract

Building on an analogy between the ageing behaviour of magnetic systems and growing interfaces, the Arcetri model, a new exactly solvable model for growing interfaces is introduced, which shares many properties with the kinetic spherical model. The long-time behaviour of the interface width and of the two-time correlators and responses is analysed. For all dimensions $d\ne 2$, universal characteristics distinguish the Arcetri model from the Edwards-Wilkinson model, although for $d>2$ all stationary and non-equilibrium exponents are the same. For $d=1$ dimensions, the Arcetri model is equivalent to the $p=2$ spherical spin glass. For $2<d<4$ dimensions, its relaxation properties are related to the ones of a particle-reaction model, namely a bosonic variant of the diffusive pair-contact process. The global persistence exponent is also derived.