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

References in corpus (26)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Discrete scale invariance and complex dimensions
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder RG approach of random systems
• Universal scaling behavior of non-equilibrium phase transitions
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Directed percolation criticality in turbulent liquid crystals
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Strong disorder fixed point in absorbing state phase transitions
• Critical Dynamics of the Contact Process with Quenched Disorder
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Absorbing state phase transitions with quenched disorder
• Critical behavior and Griffiths effects in the disordered contact process
• Study of the disordered one-dimensional contact process
• Violation of Scaling in the Contact Process with Quenched Disorder
• Reweighting in nonequilibrium simulations
• Nonequilibrium phase transition on a randomly diluted lattice
• Low-energy properties of aperiodic quantum spin chains
• Monte-Carlo simulations of the clean and disordered contact process in three dimensions
• Broadening of a nonequilibrium phase transition by extended structural defects
• Universality of the contact process with random dilution
• Monte-Carlo simulations of the smeared phase transition in a contact process with extended defects
• Absorbing-state phase transitions on percolating lattices
• Strong disorder renormalization group study of aperiodic quantum Ising chains
• Scaling behavior of the contact process in networks with long-range connections

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• Universality and Quantum Criticality in Quasiperiodic Spin Chains
• Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments
• Contact process with temporal disorder
• Continuous and discontinuous absorbing-state phase transitions on Voronoi-Delaunay random lattices
• 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
• Contact process with aperiodic temporal disorder
• Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects