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

The 2d XY model exhibits an essential phase transition, which was predicted long ago -by Berezinskii, Kosterlitz and Thouless (BKT) -to be driven by the (un)binding of vortex-anti-vortex pairs. This transition has been confirmed for the standard lattice action, and for actions with distinct couplings, in agreement with universality. Here we study a highly unconventional formulation of this model, which belongs to the class of topological lattice actions: it does not have any couplings at all, but just a constraint for the relative angles between nearest neighbour spins. By means of dynamical boundary conditions we measure the helicity modulus Υ, which shows that this formulation performs a BKT phase transition as well. Its finite size effects are amazingly mild, in contrast to other lattice actions. This provides one of the most precise numerical confirmations ever of a BKT transition in this model. On the other hand, up to the lattice sizes that we explored, there are deviations from the spin wave approximation, for instance for the Binder cumulant U 4 and for the leading finite size correction to Υ. Finally we observe that the (un)binding mechanism follows the usual pattern, although free vortices do not require any energy in this formulation. Due to that observation, one should reconsider an aspect of the established picture, which estimates the critical temperature based on this energy requirement.

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“…In this case, even the leading power of this logarithmic term differs between the standard action and topological actions [28].…”

Section: Critical Value Of the Helicity Modulusmentioning

confidence: 96%

Berezinskii–Kosterlitz–Thouless transition with a constraint lattice action

Bietenholz¹,

Gerber²,

Rejón-Barrera³

2013

J. Stat. Mech.

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“…The essential features of walking technicolor models are shared by this toy model and can be accurately investigated by numerical simulations. Optimized lattice actions have also been studied intensively in [25] for 2-d O(N ) models, where it has been shown that cut-off effects can be reduced to the per mille level. A topological lattice action has also been used in a recent study of 4-d U (1) gauge theory, to demonstrate that the correct continuum limit is obtained, to examine the effect of the lattice action on monopole condensation in the confined phase, and to test a method to measure the free energy [26].…”

Section: Jhep03(2016)116mentioning

confidence: 99%

“…One of them is used to set the lattice spacing a, the other to estimate the size of the cut-off effects at the given resolution. For the 2-d O(N ) spin model these were [25] the mass gap measured on a long strip with spatial sizes L and 2L (cf. step scaling function, [27]).…”

Section: Determination Of the Parameters Of The Actionmentioning

confidence: 99%

An improved single-plaquette gauge action

Banerjee

Bögli

Holland

et al. 2016

J. High Energ. Phys.

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Abstract:We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N ) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects.

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“…In a recent paper [8] a class of models was identified with very small lattice artifacts. Some of these models are particularly fascinating since they seem to belong to the same universality class as the standard-type actions described above but don't have the usual classical limit and so far a perturbative treatment for them is unknown (see subsection 1.2).…”

Section: Contentsmentioning

confidence: 99%

Symanzik effective actions in the large N limit

Balog

Niedermayer

Weisz

2013

J. High Energ. Phys.

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Symanzik effective actions, conjectured to describe lattice artifacts, are determined for a class of lattice regularizations of the non-linear O(N) sigma model in two dimensions in the leading order of the 1/N-expansion. The class of actions considered includes also ones which do not have the usual classical limit and are not (so far) treatable in the framework of ordinary perturbation theory. The effective actions obtained are shown to reproduce previously computed lattice artifacts of the step scaling functions defined in finite volume, giving further confidence in Symanzik's theory of lattice artifacts.Comment: 44 page

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

Cited by 12 publications

References 55 publications

Berezinskii–Kosterlitz–Thouless transition with a constraint lattice action

Berezinskii–Kosterlitz–Thouless transition with a constraint lattice action

An improved single-plaquette gauge action

Symanzik effective actions in the large N limit

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