Robustness of first-order phase transitions in one-dimensional long-range contact processes

Mean-field theory for the long-range contact process with diffusion

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 L lattice sites. The phase diagram of the model for values of L 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 L≥3 are able to reveal the suppression of the phase coexistence induced by diffusion, however, in the high-diffusion regime, larger values of L 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.

Effect of diffusion in one-dimensional discontinuous absorbing phase transitions

It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion of diffusion in the simplest one-dimensional model with a discontinuous absorbing phase transition, namely, the long-range contact process (σ-CP). Particles interact as in the usual CP, but the transition rate depends on the length ℓ of inactive sites according to 1+aℓ(-σ), where a and σ are control parameters. The inclusion of diffusion in this model has been investigated by numerical simulations and mean-field calculations. Results show that there exists three distinct regimes. For sufficiently low and large σ's the transition is, respectively, always discontinuous or continuous, independently of the strength of the diffusion. On the other hand, in an intermediate range of σ's, the diffusion causes a suppression of the phase coexistence leading to a continuous transition belonging to the directed percolation universality class.