Adler’s overrelaxation algorithm for Goldstone bosons

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Abstract
A very simple derivation of a closed-form solution to the stochastic evolution defined by Adler’s overrelaxation algorithm is given for free massive and massless scalar fields on a finite lattice with periodic boundary conditions and checkerboard updating. It is argued that the results are directly relevant when critical slowing down reflects the existence of Goldstone bosons in the system.