https://doi.org/10.1140/epjc/s10052-017-4839-0
Regular Article - Theoretical Physics
SMD-based numerical stochastic perturbation theory
1
Dipartimento di Fisica, Università di Milano-Bicocca and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126, Milan, Italy
2
Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
3
AEC, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
* e-mail: mattia.dalla.brida@desy.de
Received:
20
March
2017
Accepted:
13
April
2017
Published online:
13
May
2017
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.
© The Author(s), 2017
