Abstract
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D≳0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D≳0. © 1996 The American Physical Society.
- Received 8 February 1996
DOI:https://doi.org/10.1103/PhysRevE.54.112
©1996 American Physical Society