ABSTRACT
Theoretical studies often involve mappings of the original system onto an equivalent description in terms of abstract mathematical/graphical objects, where ‘equivalent’ means one obtains the same final answer for some particular property. Path integrals, high-temperature expansions, and Feynman diagrams are the well-known examples considered in this chapter. Under such mappings, one has to deal with the infinite-dimensional configuration space having complex topology and non-local constraints which severely reduce efficiency of Monte Carlo simulations based on standard local updates. This sometimes leads to ergodicity problems in large systems when the entire configuration space can not be sampled in a reasonable computation time. A somewhat related difficulty facing conventional Monte Carlo schemes is the computation of off-diagonal correlation functions since they have no direct relation to the configuration space of the partition function. In what follows we consider path integrals for lattice and continuous systems, high-temperature expansions, and Feynman diagrams, explain the general idea of how Worm Algorithms (WAs) deal with the topological constraints by going to the enlarged configuration space, and present illustrative results for several physics problems.
