Wavelet analysis of Ising model spin dynamics

The Burt–Adelson wavelet decomposition was used to analyze the Monte Carlo spin dynamics of a one‐dimensional Ising ring. Burt–Adelson wavelets were used because they select for spin domains and domain walls. For wavelet amplitudes c n i (t), we computed mean‐square fluctuations 〈[c n i (t)]2〉, spatial correlation functions 〈c n i (t)c n i+a (t)〉, and time correlation functions 〈c n i (t)c n i (t+τ)〉. The simulations are in excellent agreement with analytic calculations. The temperature and decomposition order dependencies of the static correlation functions are readily explained by the wavelet support L and the system’s correlation length ξ. High‐order (long‐wavelength) wavelet time correlation functions decay exponentially. Low‐order wavelet time correlation functions have an approximate two‐exponential decay, with a fast temperature‐independent relaxation corresponding to the random walk of domain edges and a slow, temperature‐dependent relaxation corresponding to domain creation and annihilation. At intermediate temperatures the slow decay rate satisfies the scaling relationship Γ−1∼〈[c n (t)]2〉 z for z=1.80. © 1995 American Institute of Physics.