Random Walks on Cayley Trees: Temperature-Induced Transience-Recurrence Transition, Small Exponents and Logarithmic Relaxation

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Published under licence by IOP Publishing Ltd
, , Citation P. Sibani and K. H. Hoffmann 1987 EPL 4 967 DOI 10.1209/0295-5075/4/9/003

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Author affiliations

1 Fysisk Institut, Odense Universitet, Campusvej 55, DK-5230 Odense M, Denmark

2 Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-6900 Heidelberg, Federal Republic of Germany

Dates

  1. Received 13 April 1987
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0295-5075/4/9/967

Abstract

Random walks on tree structures are as useful tools in physics as they are interesting themselves. Here we show that for a certain class of models they can undergo a transition from being recurrent to being transient depending on the temperature. At the transition the relaxation is logarithmic. The significance of the pole in the relaxation exponent is also discussed.

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