Two Phase Transitions for the Contact Process on Small Worlds

Details Two Phase Transitions for the Contact Process on Small Worlds Two Phase Transitions for the Contact Process on Small Worlds

2005-01-27

arxiv.org/abs/math/0501481v2

Mathematics

Probability

24 pages, 6 figures. We have rewritten the phase transition in terms of two parameters and have made improvements to our origi

Scientific paper

In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of a town where an individual's interactions at school, at work, or in social situations introduces long-range connections. However, this change dramatically alters the behavior of the contact process, producing two phase transitions. We establish this by relating the small world to an infinite "big world" graph where the contact process behavior is similar to the contact process on a tree.

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