On the absorbing-state phase transition in the one-dimensional triplet creation model

TL;DR

This paper investigates the phase transition in a one-dimensional triplet creation model, combining simulations and approximations, revealing evidence of both discontinuous and continuous transition behaviors depending on the regime.

Contribution

It introduces a detailed analysis of the triplet creation model, highlighting the potential for a continuous transition despite finite-system indications of discontinuity.

Findings

Evidence of a discontinuous phase transition at high diffusion rates

No stable interface between active and absorbing phases observed

Argument for a continuous transition based on an effective mapping

Abstract

We study the lattice reaction diffusion model 3A -> 4A, A -> 0 (``triplet creation") using numerical simulations and n-site approximations. The simulation results provide evidence of a discontinuous phase transition at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, shall nevertheless argue that the transition is continuous, despite the seemingly discontinuous phase transition suggested by studies of finite systems.