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-dimensional Ising Model using time series analysis. We have found that the signal has a Hurst exponent 0.5 in high temperatures, and it approaches 1 near the temperature TD where the damage goes to zero. We have also measured the correlation of the signal and found that it is strongly correlated near TD and describes a persistent fractional Brownian motion (FBM). Therefore the Hamming distance in the Ising model can be used to generate FBM near TD. We suggest that the system presents a 1/f spectrum in the transition temperature TD.