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No Access Submitted: 17 September 2002 Accepted: 12 December 2002 Published Online: 20 February 2003

  • Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices

J. Chem. Phys. 118, 4424 (2003); https://doi.org/10.1063/1.1543582
Ahmed E. Ismail, George Stephanopoulos, and Gregory C. Rutledge
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  • Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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  • Ahmed E. Ismail
  • George Stephanopoulos
  • Gregory C. Rutledge
  • See also: The Journal of Chemical Physics 118, 4414
    • ABSTRACT
    In this paper, we extend our analysis of lattice systems using the wavelet transform to systems for which exact enumeration is impractical. For such systems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm, which hierarchically coarse-grains a lattice model by computing the probability distribution for successively larger block spins. We demonstrate that although the method perturbs the system by changing its Hamiltonian and by allowing block spins to take on values not permitted for individual spins, the results obtained agree with the analytical results in the preceding paper, and “converge” to exact results obtained in the absence of coarse-graining. Additionally, we show that the decorrelation time for the WAMC is no worse than that of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed from data performed in several short simulations to estimate the results that would be obtained from the original simulation. Although the algorithm is not asymptotically faster than traditional MMC, the new algorithm executes several orders of magnitude faster than a full simulation of the original problem because of its hierarchical design. Consequently, the new method allows for rapid analysis of a phase diagram, allowing computational time to be focused on regions near phase transitions.

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