Comments on "Critical Study on the Absorbing Phase Transition in a Four-State Predator-Prey Model in One Dimension"

TL;DR

This paper clarifies that in a four-state predator-prey model, the predator density exhibits directed percolation critical behavior, confirming it as a valid order parameter after transient dynamics.

Contribution

The authors demonstrate that the predator density is the appropriate order parameter for the model, settling to DP critical exponents, countering previous claims about multiple absorbing states.

Findings

Predator density reaches DP critical exponents after transients.

Only the predator-free configuration is dynamically accessible as an absorbing state.

Predator density is a valid order parameter for the model.

Abstract

In a recent article [arXiv:1108.5127] Park has shown that the four-state predator-prey model studied earlier in [J. Stat. Mech, L05001 (2011)] belongs to Directed Percolation (DP) universality class. It was claimed that predator density is not a reasonable order parameter, as there are many absorbing states; a suitably chosen order parameter shows DP critical behavior. In this article, we argue that the configuration that does not have any predator is the only dynamically accessible absorbing configuration, and the predator density too settles to DP critical exponents after a long transient.