Produção Nacional
Critical behavior of a two-species reaction-diffusion problem
2000; American Physical Society; Volume: 61; Issue: 6 Linguagem: Inglês
10.1103/physreve.61.6330
ISSN1538-4519
AutoresJ. E. de Freitas, L. S. Lucena, L. R. da Silva, H. J. Hilhorst,
Tópico(s)Material Dynamics and Properties
ResumoWe present a Monte Carlo study in dimension $d=1$ of the two-species reaction-diffusion process $A+\stackrel{\ensuremath{\rightarrow}}{B}2B$ and $\stackrel{\ensuremath{\rightarrow}}{B}A.$ Below a critical value ${\ensuremath{\rho}}_{c}$ of the conserved total density $\ensuremath{\rho}$ the system falls into an absorbing state without B particles. Above ${\ensuremath{\rho}}_{c}$ the steady state B particle density ${\ensuremath{\rho}}_{B}^{\mathrm{st}}$ is the order parameter. This system is related to directed percolation but in a different universality class identified by Kree et al. [Phys. Rev. A 39, 2214 (1989)]. We present an algorithm that enables us to simulate simultaneously the full range of densities $\ensuremath{\rho}$ between zero and some maximum density. From finite-size scaling we obtain the steady state exponents $\ensuremath{\beta}=0.435(10),\ensuremath{\nu}=2.21(5),$ and $\ensuremath{\eta}=\ensuremath{-}0.606(4)$ for the order parameter, the correlation length, and the critical correlation function, respectively. Independent simulation indicates that the critical initial increase exponent takes the value ${\ensuremath{\theta}}^{\ensuremath{'}}=0.30(2),$ in agreement with the theoretical relation ${\ensuremath{\theta}}^{\ensuremath{'}}=\ensuremath{-}\ensuremath{\eta}/2$ due to Van Wijland et al. [Physica A 251, 179 (1998)].
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