Coarse grained approach for universality classification of discrete models

Details Coarse grained approach for universality classification of discrete models Coarse grained approach for universality classification of discrete models

2011-10-13

arxiv.org/abs/1110.3035v2

Physics

Condensed Matter

Statistical Mechanics

6 pages, 3 figures

Scientific paper

Discrete and continuous models belonging to a universality class share the same linearities and (or) nonlinearities. In this work, we propose a new approach that allows for calculating coarse grained coefficients and hence to determine the universality class of unrestricted and restricted discrete models. Therefor we apply small constant translations in a test space and show how to obtain the coarse grained coefficients from the transformed average interface growth velocity. Using the examples of the ballistic deposition (BD) model and the restricted solid-on-solid (RSOS) model, both belonging to the Kardar-Parisi-Zhang (KPZ) universality class, we demonstrate how to apply our approach to calculate analytically the corresponding coefficients of the KPZ equation. Our analytical nonlinear coefficients are in agreement with numerical results obtained by Monte Carlo simulations. In addition to the BD and the RSOS we study a competitive RSOS model that shows crossover regimen between the KPZ and Edwards-Wilkinson universality class.

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