Optimal Multigrid Algorithms for Variable-Coupling Isotropic Gaussian Models

A novel class of multigrid algorithms for the variable coupling isotropic Gaussian models is presented In addition to the elimination of the critical slowing down which otherwise might become much worse than usual in the case of strongly varying coupling values the vol ume factor is also eliminated That is the need to produce many independent ne grid con gurations for averaging out their statisti cal deviations is removed by applying multigrid cycles that sample mostly on coarse grids Thermodynamic limits can be calculated to relative accuracy r in just O r computer operations where r is the error relative to the standard deviation of the observable In this paper such an optimal algorithm is obtained for the calculation of the susceptibility in the d dimensional variable coupling isotropic Gaussian model with numerical experiments for d Some ba sic general rules for the operation of multigrid algorithms applicable to much wider classes of models are derived