Compact parity conserving percolation in one-dimension

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.

7 pages, 7 figures embedded in the latex, final form before J.Phys.A publication

References in corpus (2)

• Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks
• Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions

Cited by in corpus (6)

• Universality classes in nonequilibrium lattice systems
• Critical behaviour of the 1d annihilation fission process 2A->0, 2A->3A
• Critical behaviour of annihilating random walk of two species with exclusion in one dimension
• Local scale invariance in the parity conserving nonequilibrium kinetic Ising model
• On the absorbing-state phase transition in the one-dimensional triplet creation model
• Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice