Drastic reduction of cutoff effects in 2-d lattice O(N) models

J. Balog, F. Niedermayer, M. Pepe, P. Weisz, U. J. Wiese

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle δ. We fix δ by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the θ-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling g R and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = ∞ in 2-d.

Original languageEnglish
Article number140
JournalJournal of High Energy Physics
Volume2012
Issue number11
DOIs
Publication statusPublished - Nov 2012

Fingerprint

cut-off
scaling
vacuum effects
fixing
artifacts
continuums

Keywords

  • Lattice Quantum Field Theory
  • Sigma Models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Drastic reduction of cutoff effects in 2-d lattice O(N) models. / Balog, J.; Niedermayer, F.; Pepe, M.; Weisz, P.; Wiese, U. J.

In: Journal of High Energy Physics, Vol. 2012, No. 11, 140, 11.2012.

Research output: Contribution to journalArticle

Balog, J. ; Niedermayer, F. ; Pepe, M. ; Weisz, P. ; Wiese, U. J. / Drastic reduction of cutoff effects in 2-d lattice O(N) models. In: Journal of High Energy Physics. 2012 ; Vol. 2012, No. 11.
@article{bcade0dc5768467695b95ed8ed0baa85,
title = "Drastic reduction of cutoff effects in 2-d lattice O(N) models",
abstract = "We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle δ. We fix δ by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the θ-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling g R and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = ∞ in 2-d.",
keywords = "Lattice Quantum Field Theory, Sigma Models",
author = "J. Balog and F. Niedermayer and M. Pepe and P. Weisz and Wiese, {U. J.}",
year = "2012",
month = "11",
doi = "10.1007/JHEP11(2012)140",
language = "English",
volume = "2012",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "11",

}

TY - JOUR

T1 - Drastic reduction of cutoff effects in 2-d lattice O(N) models

AU - Balog, J.

AU - Niedermayer, F.

AU - Pepe, M.

AU - Weisz, P.

AU - Wiese, U. J.

PY - 2012/11

Y1 - 2012/11

N2 - We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle δ. We fix δ by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the θ-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling g R and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = ∞ in 2-d.

AB - We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle δ. We fix δ by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the θ-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling g R and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = ∞ in 2-d.

KW - Lattice Quantum Field Theory

KW - Sigma Models

UR - http://www.scopus.com/inward/record.url?scp=84881276116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881276116&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2012)140

DO - 10.1007/JHEP11(2012)140

M3 - Article

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 140

ER -