A numerical and theoretical study of multilevel performance for two-point correlator calculations
A numerical and theoretical study of multilevel performance for two-point correlator calculations
An investigation of the performance of the multilevel algorithm in the approach to criticality has been undertaken using the Ising model, performing simulations across a range of temperatures. Numerical results show that the performance of multilevel in this system deteriorates as the correlation length is increased with respect to the lattice size. The statistical error of the longest correlator in the system is reduced in a multilevel setup when the correlation length is less than one-tenth of the lattice size, while for longer correlation lengths multilevel performs more poorly than a computer-time equivalent single level algorithm. A theoretical model of this performance scaling is outlined, and shows remarkable accuracy when compared to numerical results. This theoretical model may be applied to other systems with more complex spectra to predict if multilevel techniques are likely to result in improved statistics.
hep-lat
Kitching-Morley, Ben
2fae2631-6c01-4522-800f-44308ea5ecf1
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
5 January 2022
Kitching-Morley, Ben
2fae2631-6c01-4522-800f-44308ea5ecf1
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
[Unknown type: UNSPECIFIED]
Abstract
An investigation of the performance of the multilevel algorithm in the approach to criticality has been undertaken using the Ising model, performing simulations across a range of temperatures. Numerical results show that the performance of multilevel in this system deteriorates as the correlation length is increased with respect to the lattice size. The statistical error of the longest correlator in the system is reduced in a multilevel setup when the correlation length is less than one-tenth of the lattice size, while for longer correlation lengths multilevel performs more poorly than a computer-time equivalent single level algorithm. A theoretical model of this performance scaling is outlined, and shows remarkable accuracy when compared to numerical results. This theoretical model may be applied to other systems with more complex spectra to predict if multilevel techniques are likely to result in improved statistics.
Text
2201.01610v1
- Author's Original
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Published date: 5 January 2022
Additional Information:
9 pages, 4 figures, a proceedings paper for a talk given at the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021. Submitted to Proceedings of Science, see https://pos.sissa.it/
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hep-lat
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Local EPrints ID: 469140
URI: http://eprints.soton.ac.uk/id/eprint/469140
PURE UUID: 1ab8eaa8-55e1-4cd1-879d-5bca040bc760
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Date deposited: 07 Sep 2022 17:37
Last modified: 17 Mar 2024 02:59
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Author:
Ben Kitching-Morley
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