Correlation analysis of the damage spreading problem in a 2-dimensional Ising model

We have studied the time dependence of the damage-spreading in a 2-dimensio nal Ising Model using time series analysis. We have found that the signal h as a Hurst exponent 0.5 in high temperatures, and it approaches 1 near the temperature T-D where the damage goes to zero. We have also measured the co rrelation of the signal and found that it is strongly correlated near To an d describes a persistent fractional Brownian motion (FBM). Therefore the Ha mming distance in the Ising model can be used to generate FBM near T-D. We suggest that the system presents a 1/f spectrum in the transition temperatu re T-D. (C) 1999 Elsevier Science B.V. All rights reserved.