Volume 34, Number 2, April II 1996
|Page(s)||97 - 102|
|Published online||01 September 2002|
Branching annihilating Lévy flights: Irreversible phase transitions with long-range exchanges
Instituto de Investigaciones
Fisicoquímicas Teóricas y Aplicadas (INIFTA), Facultad de
Ciencias Exactas, Universidad Nacional de La Plata, Sucursal 4, Casilla de
Correo 16, (1900) La Plata, Argentina
Accepted: 26 February 1996
The branching annihilation walk (BAW) process is generalized allowing either the particles or the offsprings (or both) to undergo Lévy flights, where the flying length (l) is a random variable with a probability distribution given by where d is the spatial dimension and σ is the dimension of the random walk. The proposed branching annihilating Lévy flights (BALF) process exhibits irreversible phase transitions between an active stationary state and a vacuum state. For short-ranged flights the model belongs to the universality class of directed percolation (DP) as the standard BAW process. However, for smaller values of σ, when the Lévy walkers undergo long-range flights exhibiting superdiffusive behaviour, the critical exponents of the BALF model depart from those of DP indicating that the Lévy mechanism effectively builds up additional long-range correlations. It is suggested that transitions of the BALF model may belong to a superuniversality class of DP where the exponents are tunable functions of σ.
PACS: 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 05.50.+q – Lattice theory and statistics; Ising problems / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, 1996
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