Hidden percolation transition in kinetic replication process

TL;DR

This paper introduces a one-dimensional kinetic contact process exhibiting two adjacent active phases with a hidden percolation transition, analyzed through mean-field and Monte Carlo simulations, revealing novel critical behavior.

Contribution

It uncovers a hidden percolation transition in a 1D kinetic process with two active phases, expanding understanding of phase transitions in low-dimensional systems.

Findings

Identification of two active phases with a second-order transition

Discovery of a hidden percolating order in one active phase

Both phase transitions belong to the directed percolation universality class

Abstract

The one-dimensional kinetic contact process with parallel update is introduced and studied by the mean-field approximation and Monte Carlo (MC) simulations. Contrary to a more conventional scenario with single active phase for 1d models with Ising-like variables, we find two different adjacent active phases in the parameter space of the proposed model with a second-order transition between them and a multiphase point where the active and the absorbing phases meet. While one of the active phases is quite standard with a smooth average filling of the space-time lattice, the second active phase demonstrates a very subtle (hidden) percolating order which becomes manifest only after certain transformation from the original model. We determine the percolation order parameter for active-active phase transition and discuss such hidden orders in other low-dimensional systems. Our MC data demonstrate finite-size critical and near-critical scaling of the order parameter relaxation for the two phase transitions. We find three independent critical indices for them and conclude that they both belong to the directed percolation universality class.