Abstract
The spreading of a globally distributed damage, created in the stationary regime, is studied in a single-component irreversible reaction process, i.e., the BK model [Browne and Kleban,Phys. Rev. A 40, 1615 (1989)]. The BK model describes one variant of the A+A→A2 reaction process on a lattice in contact with a reservoir of A species. The BK model has a single parameter, namely the rate of arrival of A species to the lattice (Y). The model, exhibits an irreversible phase transition between a stationary reactive state with production of A2 species and a poisoned state with the lattice fully covered by A species. The transition takes place at critical points (Y C ) which solely depend on the Euclidean dimensiond. It is found that the system is immune ford=1 andd=2, in the sense that even 100% of initial damage is healed within a finite healing period (T H ). Within the reactive regime,T H diverges when approachingY C according toT H ∞ (Y C −Y)−α, with α⋟1.62 and α⋟1.08 ford=1 andd=2, respectively. Ford=3 a frozen-chaotic transition is found close toY s ⋟0.4125, i.e., well inside the reactive regime 0≤Y≤Y C ⋟0.4985. Just atY S the damageD(t) heals according toD(t) ∞t −δ, with δ⋟0.71. For the frozen-chaotic transition atd=3 the order parameter critical exponent β⋟0.997 is determined.
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Communicated by J. L. Lebowitz
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Albano, E.V. Damage spreading in a single-component irreversible reaction process: Dependence of the system's immunity on the Euclidean dimension. J Stat Phys 78, 1147–1155 (1995). https://doi.org/10.1007/BF02183707
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DOI: https://doi.org/10.1007/BF02183707