New Coarse Grained Approach for Discrete Surface Models

D. HANSMANN; R. C. BUCETA

Viña del Mar

Workshop; 14th Workshop on Instabilities and non-linear structures; 2013

Universidad de Chile - CONICyT - otros

Models of interface motion are usually grouped into universality classes according to the scaling exponents of their observables (e.g. interface width, correlations, or power spectrum) and the continuous stochastic differential equations (SDE) of these universality classes describe distinctive mesoscopic properties of their underlying discrete models. But apart from these mesoscopic aspects it is not trivial to show the linkage between a discrete model and its continuous SDE. An approach to this problem is to derive a continuous SDE directly from a discrete model, taking advantage of symmetries and coarse-grained contributions. A practice, which is based on analytical functions, was introduced by Vvedensky et al. in 1993 (Phy. Rev. E 42,852), using regularization techniques of Heaviside functions derived from the first and second transition moments. A different approach, which is based on the direct calculation of the continuous SDE coefficients, has been introduced by us in 2012 (J. Phys. A 45, 435202). To this end our approach employs the probability distributions of height-differences between neighbor sites at the surface of a modeled system and generalized functions derived from the evolution rules of the model. So far, the approach has been successfully applied to both restrictive and non restrictive growth models within KPZ universality class and to volume conserving surface models with symmetrical and asymmetrical jump rates. The present work discusses the principles of the formalism on the basis of some examples and gives an outlook for future applications.