Issue |
Europhys. Lett.
Volume 34, Number 2, April II 1996
|
|
---|---|---|
Page(s) | 97 - 102 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i1996-00422-6 | |
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
Received:
21
November
1995
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.