Dynamic Phase Transition in the Contact Process with Spatial Disorder: Griffths Phase and Complex Persistence Exponents

Abstract

We present a model which displays Griffiths phase i.e. algebraic decay of density with continuously varying exponent in the absorbing phase. In active phase, the memory of initial conditions is lost with continuously varying complex exponent in this model. This is 1-D model where fraction r of sites obey rules leading to directed percolation (DP) class and the rest evolve according to rules leading to compact directed percolation (CDP) class. For infection probability $p<p_c$, the fraction of active sites $\rho (t)=0$ asymptotically. For $p>p_c$, $\rho (infty)>0$. At $p=p_c$, $\rho (t)$, the survival probability from single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence $P_l(\infty )>0$ for $p<p_c$ and $P_l(\infty )=0$ for $p>p_c$. For $p>p_s$, local persistence $P_l(t)$ decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as $p\to 1$. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increases with p. We note that underlying lattice or disorder does not have self-similar structure.

References in corpus (16)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Discrete scale invariance and complex dimensions
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder fixed point in absorbing state phase transitions
• Disorder-induced rounding of certain quantum phase transitions
• 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
• On possible experimental realizations of directed percolation
• Discovery of Log-Periodic Oscillations in Ultra-Quantum Topological Materials
• Persistence at the onset of spatiotemporal intermittency in coupled map lattices
• Spatial Log Periodic Oscillations of First-Passage Observables in Fractals
• Short-time critical dynamics of the Baxter-Wu model
• Local Persistence in the Directed Percolation Universality Class
• Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations
• Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons

Cited by in corpus (6)

• The emergence of Logarithmic-periodic oscillations in Contact process with the topological disorder
• Scaling of local persistence in the disordered contact process
• Persistence discontinuity in disordered contact processes with long-range interactions
• Approach to zigzag and checkerboard patterns in spatially extended systems
• Renormalization theory of disordered contact processes with heavy-tailed dispersal
• Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal