Phys. Rev. E 54, 112–126 (1996)Spherically symmetric random walks. II. Dimensionally dependent critical behaviorReceived 8 February 1996; published in the issue dated July 1996 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. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.54.112
DOI:
10.1103/PhysRevE.54.112
PACS:
05.40.+j, 05.20.-y, 05.50.+q
See AlsoSee Also: Carl M. Bender, Fred Cooper, and Peter N. Meisinger, Spherically symmetric random walks. I. Representation in terms of orthogonal polynomials, Phys. Rev. E 54, 100 (1996). |
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.