Spherical model of growing interfaces
arXiv:1501.07745 · doi:10.1088/1742-5468/2015/05/P05022
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 , universal characteristics distinguish the Arcetri model from the Edwards-Wilkinson model, although for all stationary and non-equilibrium exponents are the same. For dimensions, the Arcetri model is equivalent to the spherical spin glass. For 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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