Dealing with transients in models with self-organized criticality

The problems of identifying and eliminating long transients are common to various numerical models in statistical mechanics. These problems are particularly relevant for models of self-organized criticality, as the Olami–Feder–Christensen (OFC) model, for which most of the results were, and still are, obtained through numerical simulations. In order to obtain reliable numerical results, it is usually necessary to simulate models on lattices as large as possible. However, in general, this is not an easy task, because transients increase fast with lattice size. So it is often necessary to wait long computer runs to obtain good statistics. In this paper we present an efficient algorithm to reduce transient times and to identify with a certain degree of precision if the statistical stationary state is reached, avoiding long runs to obtain good statistics. The efficiency of the algorithm is exemplified in the OFC model for the dynamics of earthquakes, but it can be useful as well in many other situations. Our analysis also shows that the OFC model approaches stationarity in qualitatively different ways in the conservative and non-conservative cases.