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 → ABk and B → 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≥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.

Competition between dynamic ordering and disordering for vortices driven by superimposed ac and dc forces

“…To obtain stronger evidence for our view mentioned in this work and deeper insight into the phenomena, further experiments, such as exploring direct visualization of the vortex configuration [52,59], as well as theoretical investigation, may be needed. We believe that the present study will stimulate similar experiments and analysis in other systems where the dynamic ordering and disordering would be observed [10,16,41,48,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”

Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings

“…This is in agreement with the behavior of the aperiodic quantum Ising chain 38 and also, in the context of nonequilibrium transitions to an absorbing state, of the aperiodic contact process. 39 Furthermore, due to the fact that the critical point corresponds to a bare bond ratio of order unity, estimates of the critical exponents of the transition from the (perturbative) SDRG scheme are both technically quite difficult and unreliable. Any calculations of such quantities by numerical methods are left for future work.…”

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

“…Since 1988, the electronic properties of GF chains have been investigated [66] and the RSRM was applied for calculating the average Green's function [67,68], local [69][70][71][72][73], and integrated [74,75] density of states, as well as for analyzing the localization of eigenstates [76]. Nonequilibrium phase transitions were analyzed by means of RSRM and Monte Carlo approaches [77]. Recently, the ballistic transport was found at the center of energy spectra in macroscopic GF chains with bond disorder every six generations when v = 1 or all generations when u and v are both even numbers [78], whose wave-function localization and electrical conductivities (DC and AC) were investigated through a system length scaling analysis [79].…”