Frustration-induced phase-transition in high-dimensional deterministic cellular-automata

Frustration is introduced in high-dimensional periodic and quasi-periodic cellular automata (CA) by quenching two competing rules. It is found that at high concentration of one rule, the cyclic behaviour of the cellular automata remains determined by the rule followed by the majority of sites. For CA with a significant concentration of both rules, the macroscopic magnetisation collapses to a fixed non-zero value while microscopic time autocorrelation functions still display slow power law decay, indicating the presence of a new complex phase induced by frustration.