dorsal/arxiv
View SchemaMultiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices
| Authors | Ahmed E. Ismail, George Stephanopoulos, Gregory C. Rutledge |
|---|---|
| Categories | |
| ArXiv ID | physics/0212067 |
| URL | https://arxiv.org/abs/physics/0212067 |
| DOI | 10.1063/1.1543582 |
| Journal | J. Chem. Phys., 118 (2003) 4424 |
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, because of its hierarchical design, the new algorithm executes several orders of magnitude faster than a full simulation of the original problem. 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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"abstract": "In this paper, we extend our analysis of lattice systems using the wavelet\ntransform to systems for which exact enumeration is impractical. For such\nsystems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm,\nwhich hierarchically coarse-grains a lattice model by computing the probability\ndistribution for successively larger block spins. We demonstrate that although\nthe method perturbs the system by changing its Hamiltonian and by allowing\nblock spins to take on values not permitted for individual spins, the results\nobtained agree with the analytical results in the preceding paper, and\n``converge\u0027\u0027 to exact results obtained in the absence of coarse-graining.\nAdditionally, we show that the decorrelation time for the WAMC is no worse than\nthat of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed\nfrom data performed in several short simulations to estimate the results that\nwould be obtained from the original simulation. Although the algorithm is not\nasymptotically faster than traditional MMC, because of its hierarchical design,\nthe new algorithm executes several orders of magnitude faster than a full\nsimulation of the original problem. Consequently, the new method allows for\nrapid analysis of a phase diagram, allowing computational time to be focused on\nregions near phase transitions.",
"arxiv_id": "physics/0212067",
"authors": [
"Ahmed E. Ismail",
"George Stephanopoulos",
"Gregory C. Rutledge"
],
"categories": [
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1063/1.1543582",
"journal_ref": "J. Chem. Phys., 118 (2003) 4424",
"title": "Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices",
"url": "https://arxiv.org/abs/physics/0212067"
},
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