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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 74 (1994), S. 313-348 
    ISSN: 1572-9613
    Keywords: Multigrid ; Gaussian model ; Ising spin model ; XY model ; Monte Carlo ; thermodynamic limit ; coarsening by approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1435-1536
    Keywords: Thalliumsoaps ; X-raydiffraction ; latticeparameters ; unitcell ; phasebehavior ; polymorphism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The results of X-ray diffraction patterns of homologous thallium soaps TlC n (n-8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20 and 22) in dependence on the temperature showed that the structures of the phases below the temperature range of the liquid-crystalline neat phase (so called phase C1, phase C2, phase I, phase II) are crystalline-like, not liquid-crystalline. As function of the chain length of the fatty acid group, we found the following phase sequences to be a function of temperature: TlC8: phase I↔neat phase: TlC9−Tl14: phase C2↔phase II↔phase I↔neat phase; TlC15, TlC16: phase C1↔phase II↔phase I↔neat phase; TlC17−TlC22: phase C1↔phase II↔neat phase. From the X-ray patterns of the thallium soaps were calculated the lattice parameters and the unit cells of these homologues at various temperatures. The comparison between the lattice parameters of the homologues showed, surprisingly, that these parameters were independent of chain length and temperature. This X-ray data are the basis for the following development of structure models of the phase C1, phase C2, phase I, and phase II, including the neat phase (see Part 2).
    Type of Medium: Electronic Resource
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