Spherically symmetric random walks. II. Dimensionally dependent critical behavior

Journal Article · Mon Jul 01 04:00:00 EDT 1996 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.54.112· OSTI ID:285910

Bender, C M ^[1]; Boettcher, S ^[2]; Meisinger, P N ^[1]

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1. Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)
2. Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 (United States)

A recently developed model of random walks on a {ital D}-dimensional hyperspherical lattice, where {ital D} is {ital 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 {ital D}{approx_gt}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 {ital D}{approx_gt}0. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 285910
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 1 Vol. 54; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

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BROWNIAN MOVEMENT
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