Spherical model of growing interfaces

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 ≠ 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.