Mori–Zwanzig–Daubechies decomposition of Ising‐model Monte Carlo dynamics

Monte Carlo dynamics of one‐ and two‐dimensional Ising lattices were studied by computer simulation. A comparison of decompositions made with Haar and Daubechies wavelets finds that wavelet–wavelet time correlation functions 〈cⁿ(t)cⁿ(t+τ)〉 and their long‐time decay constants Γ_n are virtually independent of the choice of wavelet basis. An intermediate‐temperature scaling relation between Γ_n and 〈cⁿ(t)cⁿ(t+τ)〉 fails at low temperature. The temperature at which failure occurs decreases with increasing wavelet decimation level n. Mori–Zwanzig memory kernels φ(τ) are extracted from 〈cⁿ(t)cⁿ(t+τ)〉 without resort to Laplace transforms. Numerically, φ(τ) computed from the random force autocorrelation function 〈 f_i(t)f_i(t+τ)〉 is in good agreement with φ(τ) computed from the 〈cⁿ(t)cⁿ(t+τ)〉. Even for a system as simple as the two‐dimensional periodic Ising lattice with nearest‐neighbor interactions, φ(τ) is nonexponential; our results are consistent with a power‐law decay of φ(τ) at large τ. © 1995 American Institute of Physics.