Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations

Abstract

We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB${}^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.

12 pages, 9 eps figures included, final version as published

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• Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings
• Dynamic Phase Transition in the Contact Process with Spatial Disorder: Griffths Phase and Complex Persistence Exponents
• Emergent dimerization and localization in disordered quantum chains
• Contact process with simultaneous spatial and temporal disorder
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• Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects