Abstract
The effect of diffusion in the one-dimensional long-range contact process is investigated by mean-field calculations. Recent works have shown that diffusion decreases the effectiveness of long-range interactions, affecting the character of the phase transition: for higher values of the diffusion coefficient, stronger long-range interactions are required to enable phase coexistence and first-order behavior. Here we apply a generalized mean-field approximation for the master equation of the model that considers states of an aggregate of lattice sites. The phase diagram of the model for values of up to 10 is obtained, and for some values of the diffusion rate extrapolations to infinite-sized systems are given. For low-diffusive systems, approximations with are able to reveal the suppression of the phase coexistence induced by diffusion, however, in the high-diffusion regime, larger values of are necessary to correctly account for the higher range of correlations. We present a very efficient method to study the mean-field equations and determine the nature of the phase transitions that may be of general utility.
- Received 10 February 2015
DOI:https://doi.org/10.1103/PhysRevE.92.032131
©2015 American Physical Society