On the phase diagram of frustrated (quasi-)periodic cellular automata. (English) Zbl 0901.60082

Mousseau, Normand

J. Phys. A, Math. Gen. 29, No. 12, 3021-3036 (1996).

Summary: 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 quasiperiodic 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, \(p(\text{P}2)\simeq 0.359\), leading to a macroscopic fixed point. A second phase transition, at \(p(\text{P}2)\simeq 0.70\), 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.

MSC:

60K40	Other physical applications of random processes
68Q80	Cellular automata (computational aspects)
82B26	Phase transitions (general) in equilibrium statistical mechanics

Keywords:

periodic and quasiperiodic cycles; low concentration of impurities; stretched exponential relaxation