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An investigation of the performance of the multilevel algorithm in theapproach to criticality has been undertaken using the Ising model, performingsimulations across a range of temperatures. Numerical results show that theperformance of multilevel in this system deteriorates as the correlation lengthis increased with respect to the lattice size. The statistical error of thelongest correlator in the system is reduced in a multilevel setup when thecorrelation length is less than one-tenth of the lattice size, while for longercorrelation lengths multilevel performs more poorly than a computer-timeequivalent single level algorithm. A theoretical model of this performancescaling is outlined, and shows remarkable accuracy when compared to numericalresults. This theoretical model may be applied to other systems with morecomplex spectra to predict if multilevel techniques are likely to result inimproved statistics.

A numerical and theoretical study of multilevel performance for two-point correlator calculations