Optimal multigrid algorithms for calculating thermodynamic limits

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.