### 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 language | English |
---|---|

Article number | 140 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2012 |

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### Keywords

- Lattice Quantum Field Theory
- Sigma Models

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(11), [140]. https://doi.org/10.1007/JHEP11(2012)140

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

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2012, no. 11, 140. https://doi.org/10.1007/JHEP11(2012)140

}

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

AN - SCOPUS:84881276116

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 140

ER -