Absence of the discontinuous transition in the one-dimensional triplet creation model

TL;DR

This study uses extensive simulations to demonstrate that the one-dimensional triplet creation model exhibits a continuous transition consistent with directed percolation, refuting previous claims of a discontinuous transition.

Contribution

The paper provides numerical evidence that the one-dimensional triplet creation model does not show a discontinuous transition, aligning with theoretical predictions and clarifying its universality class.

Findings

The triplet creation model belongs to the directed percolation universality class.

The phase boundary follows a crossover from mean field to directed percolation behavior.

No evidence of a discontinuous transition was observed in extensive simulations.

Abstract

Although Hinrichsen in his unpublished work theoretically rebutted the possibility of the discontinuous transition in one-dimensional nonequilibrium systems unless there are additional conservation laws, long-range interactions, macroscopic currents, or special boundary conditions, we have recently observed the resurrection of the claim that the triplet creation model (TC) introduced by Dickman and Tom\'e [Phys. Rev. E {\bf 44}, 4833 (1991)] would show the discontinuous transition. By extensive simulations, however, we find that the one-dimensional TC does belong to the directed percolation universality class even for larger diffusion constant than the suggested tricritical point in the literature. Furthermore, we find that the phase boundary is well described by the crossover from the mean field to the directed percolation, which supports the claim that the one-dimensional TC does not exhibit a discontinuous transition.