Diagrammatic Monte Carlo and Worm Algorithm Techniques

Abstract

This chapter reviews basic principles of Diagrammatic Monte Carlo and Worm Algorithm techniques. Diagrammatic Monte Carlo establishes generic rules for unbiased sampling of well defined configuration spaces when the only source of errors is of statistical origin due to finite sampling time, no matter whether configuration parameters involve discrete, as in the Ising model, or continuous, as in Feynman diagrams or lattice path integrals, variables. Worm Algorithms allow one to sample efficiently configuration spaces with complex topology and non-local constraints which cause severe problems for Monte Carlo schemes based on local updates. They achieve this goal by working with the enlarged configuration space which includes configurations violating constraints present in the original formulation.