Rigorous lower bound on the dynamic critical exponent of some multilevel Swendsen-Wang algorithms
Xiao-Jian Li, Alan D. Sokal · Physical Review Letters · 1991
We prove the rigorous lower bound ${\mathit{z}}_{\mathrm{exp}}$\ensuremath{\ge}\ensuremath{\alpha}/\ensuremath{ u} for the dynamic critical exponent of a broad class of multilevel (or ``multigrid'') variants of the Swendsen-Wang algorithm. This proves that such algorithms do suffer from critical slowing down. We conjecture that such algorithms in fact lie in the same dynamic universality class as the stanard Swendsen-Wang algorithm.