Damage spreading in the Q2R Ising model

Abstract

We find evidence of metastability in the spreading of damage in the Q2R cellular automaton approximation for a 2D Ising system which is first equilibrated with a standard Metropolis simulation. A subsequent study of both single-site and whole-line damage spreading in Metropolis/Q2R systems as well as in pure Q2R systems shows a logarithmic dependence of the damage-spreading threshold on time, and saturation effects in single-site damage suggest a transition in the damage-spreading threshold at low initial energy values. Examination of the magnetization as a function of energy in pure Q2R shows extremely long relaxation times for p<p_c, which may bear some relation to the extremely slow convergence of the damage-spreading threshold.