Critical behaviour of random walks

Details Critical behaviour of random walks Critical behaviour of random walks

1993-12-03

arxiv.org/abs/hep-lat/9312018v2

Physical Review E 50 (1994) 91

Physics

High Energy Physics

High Energy Physics - Lattice

18 pages, DFTUZ 93.12

Scientific paper

10.1103/PhysRevE.50.91

We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical behaviour with a rich phase structure similar to spin systems. We interpret a change in the asymptotic density of particles as a phase transition. For high directionality the change is abrupt, possibly of first order. For small directionality the phase transition is of higher order. We have computed the phase diagram, the volume dependence of the critical point, and the relaxation time of the system in the large volume limit.

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