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 configu rations for averaging out their statistical deviations, by averaging o ver the many samples produced in coarse grids during the multigrid cyc le. Thermodynamic limits can be calculated to accuracy epsilon in just O(epsilon-2) computer operations. Examples described in detail and wi th results of numerical tests are the calculation of the susceptibilit y, the sigma-susceptibility, and the average energy in Gaussian models , and also the determination of the susceptibility and the critical te mperature in a two-dimensional Ising spin model. Extension to more adv anced models is outlined.