https://doi.org/10.1140/epjb/e2005-00319-8
Optimal disorder for segregation in annealed small worlds
Centro
Atómico Bariloche and Instituto Balseiro, 8400 Bariloche,
Río Negro, Argentina
Corresponding author: a gils@ib.cnea.gov.ar
Received:
2
March
2005
Revised:
10
June
2005
Published online:
11
October
2005
We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two particles. Motion is a mixture of diffusion to nearest-neighbour sites and long-range jumps, known as annealed small-world propagation. The long-range jump probability plays the role of the small-world disorder. We show that there is an optimal value of this probability, for which the segregation process is fastest. Moreover, above a critical probability, the time needed to reach a fully segregated state diverges for asymptotically large systems. These special values of the long-range jump probability depend crucially on the particle density. Our system is a novel example of the rare dynamical processes with critical behaviour at a finite value of the small-world disorder.
PACS: 89.75.Fb – Structures and organization in complex systems / 02.50.Ey – Stochastic processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005