Extended mean-field theory is used for studying the effect of nonlocal site exchange on the critical transition of the one-dimensional, stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod. Phys. 55, 6011 (1993)]. The analysis is carried out at different levels taking n-point correlations explicitly into consideration. Extrapolation to the n→ (exact) limit gives results, which agree well with simulation. By applying nonlocal site-exchange mixing the universality of the transition changes and a continuous crossover of critical point and β exponent is observed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics