Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. An investigation of the phase transitions of a family of probabilistic automata
 Advances in complex systems 7 (2004), Nr.1, S.93123 ISSN: 02195259 ISSN: 12948535 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer AIS ( IAIS) () 
Abstract
We investigate a family of totalistic probabilistic cellular automata (PCA) which depend on three parameters. For the uniform random neighborhood and for the symmetric 1D PCA the exact stationary distribution is computed for all finite n. This result is used to evaluate approximations (univariate and bivariate marginals). It is proven that the univariate approximation (also called meanfield) is exact for the uniform random neighborhood PCA. The exact results and the approximations are used to investigate phase transitions. We compare the results of two order parameters, the univariate marginal and the normalized entropy. Sometimes different transitions are indicated by the Ehrenfest classification scheme. This result shows the limitations of using just one or two order parameters for detecting and classifying major transitions of the stationary distribution. Furthermore, finite size scaling is investigated. We show that extrapolations to n = infinity from numerical calculations of finite n can be misleading in difficult parameter regions. Here, exact analytical estimates are necessary.