Continuum limit and improved action in lattice theories

Symanzik, K.

doi:10.1016/0550-3213(83)90469-8

Cited by 563 publications

(543 citation statements)

References 20 publications

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“…It is of the form Actually, this form of the local effective action for the O(n) nonlinear sigma model cannot be found in Symanzik's published papers [4,5]. But in the case of the φ 4 model an analogous local effective Lagrangian is introduced in [4] and in [5] an improved lattice action is presented for the O(n) sigma model. (3.5) is constructed using the φ 4 model analogy and has exactly the same terms as the improved action in [5].…”

Section: The Effective Lagrangianmentioning

confidence: 99%

“…(3.5) is constructed using the φ 4 model analogy and has exactly the same terms as the improved action in [5]. It is not unique: as discussed in [5] there is an ambiguity in choosing the coefficients which can be used to put (for example) W 2 and X 2 equal to zero. To be able to identify the lattice correlation functions with the ones obtained using the effective action we also have to relate the couplings λ 0 and g and the sources J a and j a , as will be discussed below.…”

Section: The Effective Lagrangianmentioning

confidence: 99%

“…But in the case of the φ 4 model an analogous local effective Lagrangian is introduced in [4] and in [5] an improved lattice action is presented for the O(n) sigma model. (3.5) is constructed using the φ 4 model analogy and has exactly the same terms as the improved action in [5]. It is not unique: as discussed in [5] there is an ambiguity in choosing the coefficients which can be used to put (for example) W 2 and X 2 equal to zero.…”

Section: The Effective Lagrangianmentioning

confidence: 99%

“…In the early 80's Symanzik was working on the nature of lattice artifacts, in particular with respect to his improvement program [4,5,6,7,8]. In this paper the general theory is not discussed; we only consider in section 3 Symanzik's theory applied to the 2-dimensional O(n) σ-model 1 .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

2010

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Lattice artifacts in the 2d O(n) non-linear σ-model are expected to be of the form O(a 2 ), and hence it was (when first observed) disturbing that some quantities in the O(3) model with various actions show parametrically stronger cutoff dependence, apparently O(a), up to very large correlation lengths. In a previous letter [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O(a 2 ) artifacts which are especially large (ln 3 a) for n = 3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3) and O(4) are also presented.

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Section: The Effective Lagrangianmentioning

confidence: 99%

Section: The Effective Lagrangianmentioning

confidence: 99%

Section: The Effective Lagrangianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

2010

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“…First one constructs the quark level effective action, including explicit nonzero a effects. Following the method of Symanzik [14], S ef f consists of all local continuum lattice operators of dimension ≤ 6 invariant under the lattice symmetries. In practice it is easiest to first determine all allowed lattice operators of dimension ≤ 6, as in Refs.…”

Section: Nlo Staggered Chiral Lagrangianmentioning

confidence: 99%

Next-to-Leading-Order Staggered Chiral Perturbation Theory

Sharpe

Water

2005

Nuclear Physics B - Proceedings Supplements

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We have extended staggered chiral perturbation theory (SχPT) to O(a 2 p 2 ), O(a 4 ), and O(a 2 m), the orders necessary for a full next-to-leading order (NLO) calculation of pseudo-Goldstone boson (PGB) masses and decay constants including taste-symmetry violations. We present predictions relating SO(4) taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. These can be used to test the 4 √ Det trick.

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A Renormalization Group Flow Approach to Decoupling and Irrelevant Operators

Kim¹

1995

Annals of Physics

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Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a φ 4 -type scalar field theory involving two real scalar fields (one is heavy with mass M and the other light). Then, to all orders in perturbation theory, it is shown that effects of virtual heavy particles up to the order 1/M 2N 0 can be systematically incorporated into light-particle theory via effective local vertices of canonical dimension at most 4 + 2N 0 . The couplings for vertices of dimension 4 + 2N are of order 1/M 2N and are systematically calculable. All this is achieved through intuitive dimensional arguments without resorting to complicated graphical arguments or convergence theorems. *

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Continuum limit and improved action in lattice theories

Cited by 563 publications

References 20 publications

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

Next-to-Leading-Order Staggered Chiral Perturbation Theory

A Renormalization Group Flow Approach to Decoupling and Irrelevant Operators

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