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

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 Menyhárd (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.

11 pages, 20 figures embedded in the text, minor changes in the text, a new table and new references are added

References in corpus (6)

• Theory of Branching and Annihilating Random Walks
• Stochastic Lattice Models with Several Absorbing States
• Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model
• Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks
• The three species monomer-monomer model: A mean-field analysis and Monte Carlo study
• Damage Spreading in the Ising Model

Cited by in corpus (8)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Critical behaviour of the 1d annihilation fission process 2A->0, 2A->3A
• Phase transition classes in triplet and quadruplet reaction diffusion models
• The relaxation of initial condition in systems with infinitely many absorbing states
• Damage spreading transition in an opinion dynamics model
• Compact parity conserving percolation in one-dimension
• Crossovers from parity conserving to directed percolation universality