Irreversible phase transitions in contact processes with Lévy exchanges and long-range interactions

The contact process (CP) is generalized allowing the exchange of particles via Lévy flights, where the flying length (l) is a random variable with a probability distribution given by P(l)∝${\mathit{l}}^{\mathrm{-}\mathit{d}\mathrm{-}\mathrm{\sigma }}$, where d is the spacial dimension and σ is the dimension of the random walk. The contact process with Lévy flights (CPLF) exhibits irreversible phase transitions between an active state and a vacuum state. It is show that within the superdiffusive regime of the walkers (i.e., σ34, 97 (1996)] and those of the CPLF gives strong evidences on a universality class which comprises second order irreversible phase transitions in systems involving Lévy exchanges and/or flights. It is suggested that the CPLF is equivalent to the standard CP with long-range interactions generated by a potential decaying with distance r as a power law of the form V(r)∝${\mathit{r}}^{\mathrm{-}\mathit{d}\mathrm{-}\mathrm{\sigma }}$. © 1996 The American Physical Society.