Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions

TL;DR

This study investigates damage spreading transitions in one-dimensional non-equilibrium models, revealing how symmetries influence critical behavior and universality classes, with distinct continuous and discontinuous transitions observed.

Contribution

It provides a comparative analysis of damage spreading in models with and without parity conservation, highlighting differences in transition types and universality classes.

Findings

Kink damage exhibits continuous PC class transition.

Spin damage shows discontinuous transition with compact clusters.

Static exponents align with PC universality at the transition.

Abstract

The damage spreading (DS) transitions of two one-dimensional stochastic cellular automata suggested by Grassberger (A and B) and the kinetic Ising model of Menyh\'ard (NEKIM) have been investigated on the level of kinks and spins. On the level of spins the parity conservation is not satisfied and therefore studying these models provides a convenient tool to understand the dependence of DS properties on symmetries. For the model B the critical point and the DS transition point is well separated and directed percolation damage spreading transition universality was found for spin damage as well as for kink damage in spite of the conservation of damage variables modulo 2 in the latter case. For the A stochastic cellular automaton, and the NEKIM model the two transition points coincide with drastic effects on the damage of spin and kink variables showing different time dependent behaviours. While the kink DS transition is continuous and shows regular PC class universality, the spin damage exhibits a discontinuous phase transition with compact clusters and PC like dynamical scaling ($\eta^,$), ($\delta_s$) and ($z_s$) exponents whereas the static exponents determined by FSS are consistent with that of the spins of the NEKIM model at the PC transition point. The generalised hyper-scaling law is satisfied.