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2018

Scaling properties of multiscale equilibration

Detmold, William, Endres, Michael G.

Understand

We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations.

The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale.
Focusing on non-topological long-distance observables in pure SU(3) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing.
Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.

Built on

N. Cabibbo and E. Marinari, Physics Letters B 119
1982
Earlier work this paper cites.
M. Lüscher, Commun. Math. Phys. 85
1982
Earlier work this paper cites.
J. Goodman and A. D. Sokal, Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
A. Phillips and D. Stone, Commun. Math. Phys. 103
1986
Earlier work this paper cites.
F. R. Brown and T. J. Woch, Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
R. G. Edwards, J. Goodman, and A. D. Sokal, Nucl. Phys. B354
1991
Earlier work this paper cites.
R. G. Edwards, S. J. Ferreira, J. Goodman, and A. D. Sokal, Nucl. Phys. B380
1992
Earlier work this paper cites.
W. Janke and T. Sauer, LATTICE 93: 11th International Symposium on Lattice Field Theory Dallas, Texas, October 12-16, 1993 , Nucl. Phys. Proc. Suppl. 34
1994
Earlier work this paper cites.
M. Grabenstein and B. Mikeska, LATTICE 93: 11th International Symposium on Lattice Field Theory Dallas, Texas, October 12-16, 1993 , Nucl. Phys. Proc. Suppl. 34
1994
Earlier work this paper cites.
M. Grabenstein and K. Pinn, Phys. Rev. D50
1994
Earlier work this paper cites.
G. ’t Hooft, Physics Letters B 349
1995
Earlier work this paper cites.