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

TL;DR

This paper investigates the robustness of first-order phase transitions in one-dimensional long-range contact processes, analyzing various models and rules to determine conditions under which discontinuous transitions occur.

Contribution

It provides a comprehensive analysis of how different long-range interactions and rules affect the nature of phase transitions in one-dimensional contact processes.

Findings

Discontinuous transitions occur for small  in models with a single absorbing state.

Presence of infinite absorbing states alters the transition scenario depending on interaction rules.

Different mechanisms of weakening long-range interactions influence the transition type.

Abstract

It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link, here we investigate thoroughly a family of long-range contact processes. They are introduced through the transition rate $1+a\ell^{-\sigma}$, where $\ell$ is the length of inactive islands surrounding particles. In the former approach we reconsider the original model (called $\sigma-$contact process), by considering distinct mechanisms of weakening the long-range interaction toward the short-range limit. Second, we study the effect of different rules, including creation and annihilation by clusters of particles and distinct versions with infinitely many absorbing states. Our results show that all examples presenting a single absorbing state, a discontinuous transition is possible for small $\sigma$. On the other hand, the presence of infinite absorbing states leads to distinct scenario depending on the interactions at the frontier of inactive sites.