TY - JOUR
T1 - Scaling of local persistence in the disordered contact process
AU - Juhász, Róbert
AU - Kovács, István A.
N1 - Funding Information:
This work was supported by the National Research, Development and Innovation Office through Grant No. K128989. I.A.K. was supported by the European Research Council Synergy under Grant No. 810115 - DYNASNET.
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/7
Y1 - 2020/7
N2 - We study the time dependence of the local persistence probability during a nonstationary time evolution in the disordered contact process in d=1, 2, and 3 dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply at the critical point analytically for d=1 and numerically for d=2,3. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal dimension-dependent generalized exponent. For d=1, the distribution of sample-dependent local persistence is shown to be characterized by a universal limit distribution of effective persistence exponents. Using a phenomenological approach of rare-region effects in the active phase, we obtain a nonuniversal algebraic decay of the average persistence for d=1 and enhanced power laws for d>1. As an exception, for randomly diluted lattices, the algebraic decay remains valid for d>1, which is explained by the contribution of dangling ends. Results on the time dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.
AB - We study the time dependence of the local persistence probability during a nonstationary time evolution in the disordered contact process in d=1, 2, and 3 dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply at the critical point analytically for d=1 and numerically for d=2,3. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal dimension-dependent generalized exponent. For d=1, the distribution of sample-dependent local persistence is shown to be characterized by a universal limit distribution of effective persistence exponents. Using a phenomenological approach of rare-region effects in the active phase, we obtain a nonuniversal algebraic decay of the average persistence for d=1 and enhanced power laws for d>1. As an exception, for randomly diluted lattices, the algebraic decay remains valid for d>1, which is explained by the contribution of dangling ends. Results on the time dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.
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U2 - 10.1103/PhysRevE.102.012108
DO - 10.1103/PhysRevE.102.012108
M3 - Article
C2 - 32795024
AN - SCOPUS:85089464888
VL - 102
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 1
M1 - 012108
ER -