Compact parity conserving percolation in one-dimension

TL;DR

This paper investigates the critical exponents and fluctuations in a one-dimensional parity-conserving percolation model, revealing significant effects on spin spreading while confirming hyperscaling relations for compact clusters.

Contribution

It provides a numerical analysis of critical exponents in the NEKIM model near the parity-conserving transition, highlighting the impact of kink fluctuations.

Findings

Critical fluctuations significantly affect spin spreading exponents.

Hyperscaling relations remain valid for compact clusters.

Numerical estimates of critical exponents near the transition point.

Abstract

Compact directed percolation is known to appear at the endpoint of the directed percolation critical line of the Domany-Kinzel cellular automaton in 1+1 dimension. Equivalently, such transition occurs at zero temperature in a magnetic field H, upon changing the sign of H, in the one-dimensional Glauber-Ising model with well known exponents characterising spin-cluster growth. We have investigated here numerically these exponents in the non-equilibrium generalization (NEKIM) of the Glauber model in the vicinity of the parity-conserving phase transition point of the kinks. Critical fluctuations on the level of kinks are found to affect drastically the characteristic exponents of spreading of spins while the hyperscaling relation holds in its form appropriate for compact clusters.