Optimal multigrid algorithms for calculating thermodynamic limits | Zendy

Achi Brandt | Zendy; Meirav Galun | Zendy; Dorit Ron | Zendy

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Optimal multigrid algorithms for calculating thermodynamic limits

Author(s) -

Achi Brandt,

Meirav Galun,

Dorit Ron

Publication year - 1994

Publication title -

journal of statistical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.71

H-Index - 115

eISSN - 1572-9613

pISSN - 0022-4715

DOI - 10.1007/bf02186816

Subject(s) - multigrid method , ising model , gaussian , grid , statistical physics , mathematics , energy (signal processing) , algorithm , computer science , physics , partial differential equation , mathematical analysis , geometry , statistics , quantum mechanics

Beyond eliminating the critical slowing down, multigrid algorithms can also eliminate the need to produce many independent fine-grid configurations for averaging out their statistical deviations, by averaging over the many samples produced in coarse grids during the multigrid cycle. Thermodynamic limits can be calculated to accuracy ɛ in justO(ε-2) computer operations. Examples described in detail and with results of numerical tests are the calculation of the susceptibility, the σ-susceptibility, and the average energy in Gaussian models, and also the determination of the susceptibility and the critical temperature in a two-dimensional Ising spin model. Extension to more advanced models is outlined.

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