Metropolis updates for Diagrammatic Monte-Carlo algorithms from Schwinger-Dyson equations
arXiv:1609.08833
Abstract
We describe a general recipe for constructing Metropolis updates for Diagrammatic Monte-Carlo (DiagMC) algorithms, based on the Schwinger-Dyson equations in quantum field theory. This approach bypasses explicit duality transformations, enumeration or classification of diagrams and can be used for lattice quantum field theories with unknown or complicated dual representations (such as non-Abelian lattice gauge theories). DiagMC algorithms constructed in this way can still be plagued by the sign problem, which is, however, completely different from the sign problem in conventional Monte-Carlo simulations and has its origin in cancellations between diagrams with positive and negative weights. To test the presented approach, we apply DiagMC to calculate the first 7 orders of 1/N expansion in the quartic matrix model and find good agreement with analytic results, with the exception of the close vicinity of the critical coupling where the critical slowing down sets in.
arXiv comment7 pages PoS style, 1 figure, to appear in the proceedings of the Lattice 2016 conference
References in corpus (7)
- Worm algorithms for classical statistical models
- Diagrammatic Monte Carlo
- A short overview of the "Topological recursion"
- Abelian color cycles: a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory
- New developments for dual methods in lattice field theory at non-zero density
- A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations
- Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes