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 $d\ne 2$, 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.

33 pages, 4 figures, minor corrections. Final form, to appear in J.Stat.Mech. 05.40.-a, 05.70.Ln, 81.10.Aj, 02.50.-r, 68.43.De

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• Large time zero temperature dynamics of the spherical p=2-spin glass model of finite size
• Dynamical symmetries and causality in non-equilibrium phase transitions
• From dynamical scaling to local scale-invariance: a tutorial
• Lindblad dynamics of a quantum spherical spin
• Analysis of etching at a solid-solid interface
• Lindblad dynamics of the quantum spherical model
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
• Universal scaling relation for growth phenomena
• Physical ageing from generalised time-translation-invariance
• Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Non-local meta-conformal invariance in diffusion-limited erosion
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model