# Scaling properties of multiscale equilibration

## Abstract

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 nontopological 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.

- Authors:

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1433463

- Alternate Identifier(s):
- OSTI ID: 1501513

- Grant/Contract Number:
- SC0010495; SC0011090; SC0018121

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 7; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Particles & Fields; Statistical Physics

### Citation Formats

```
Detmold, W., and Endres, M. G. Scaling properties of multiscale equilibration. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.074507.
```

```
Detmold, W., & Endres, M. G. Scaling properties of multiscale equilibration. United States. doi:10.1103/PhysRevD.97.074507.
```

```
Detmold, W., and Endres, M. G. Tue .
"Scaling properties of multiscale equilibration". United States. doi:10.1103/PhysRevD.97.074507.
```

```
@article{osti_1433463,
```

title = {Scaling properties of multiscale equilibration},

author = {Detmold, W. and Endres, M. G.},

abstractNote = {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 nontopological 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.},

doi = {10.1103/PhysRevD.97.074507},

journal = {Physical Review D},

number = 7,

volume = 97,

place = {United States},

year = {2018},

month = {4}

}

DOI: 10.1103/PhysRevD.97.074507

#### Figures / Tables:

_{0.4}/a, the physical value of the Sommer scale (taken to be $r$

_{0}= 0.5 fm), and the continuum conversion factor between $r$

_{0}and reference scale $w$

_{0.4}determinedmore »

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*