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 Γn are virtually independent of the choice of wavelet basis. An intermediate‐temperature scaling relation between Γn 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 〈 fi(t)fi(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.
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Research Article| March 01 1995
Mori–Zwanzig–Daubechies decomposition of Ising‐model Monte Carlo dynamics
George D. J. Phillies;
George D. J. Phillies, Jonathan Stott; Mori–Zwanzig–Daubechies decomposition of Ising‐model Monte Carlo dynamics. Comput. Phys. 1 March 1995; 9 (2): 225–234. https://doi.org/10.1063/1.168527
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