On the phase diagram of frustrated (quasi-)periodic cellular automata

Abstract

We introduce and study frustrated cellular automata (CA) obtained by quenching competing Chaté - Manneville rules. A period-two (P2) rule and a quasi-periodic one with period close to three (QP3) are frozen at random on the lattice sites. We find that the periodic and quasi-periodic cycles are resilient to internal frustration as well as to external unbounded noise. A low concentration of impurities improves the (quasi-)periodicity of the CA, damping the chaotic background noise significantly. Starting from pure QP3 CA, a first phase transition happens at a concentration of rule P2, , leading to a macroscopic fixed point. A second phase transition, at , brings the P2 phase. Although macroscopically stable, the central phase displays a stretched exponential relaxation of the site - site autocorrelations, indicating the presence of a new type of glass with slow dynamics superimposed on the natural cyclic dynamics of the CA rules. These results appear to be quite general and are found for many pairs of rules.