Testing the efficiency of different improvement programs

Caracciolo, Sergio; Montanari, Andrea; Pelissetto, Andrea

doi:10.1016/s0550-3213(99)00373-9

Cited by 5 publications

(5 citation statements)

References 73 publications

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“…This phenomenon is not new in two-dimensional models. Indeed a similar non-commutativity appears in the corrections to the finite-size scaling functions [49,50]. In the large-N limit, cf.…”

Section: Corrections In Two Dimensionsmentioning

confidence: 75%

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Mean-field expansion for spin models with medium-range interactions

1999

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We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N )-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as R −3 , R being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches.

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“…This phenomenon is not new in two-dimensional models. Indeed a similar non-commutativity appears in the corrections to the finite-size scaling functions [49,50]. In the large-N limit, cf.…”

Section: Corrections In Two Dimensionsmentioning

confidence: 75%

“…By analogy with what has been found for the finite-size scaling corrections in Refs. [49,50], we could have a behaviour of the form…”

Section: Corrections In Two Dimensionsmentioning

confidence: 99%

Mean-field expansion for spin models with medium-range interactions

1999

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“…Then, we insert Eqs. (10,16) in the MOM coupling constant definition, Eq. ( 13), where the Green functions scalar form factors are automatically renormalized in MOM prescription at the scale k 2 by the 3/2-power of Z M OM , and finally obtain 7…”

Section: Running Coupling Constantmentioning

confidence: 99%

“…A very recent lattice calculation within the two-dimensional non-linear sigma model[16] insists on the necessity of knowing the OPE coefficients at least to one loop to reach agreement with OPE predictions.10 A computation of β2 may appear soon[17].…”

mentioning

confidence: 99%

Consistent OPE description of gluon two- and three-point Green functions?

Boucaud¹,

Yaouanc²,

Leroy³

et al. 2000

Physics Letters B

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We perform an OPE analysis of the flavorless non-perturbative gluon propagator and the symmetric three-gluon vertex in the Landau gauge. The first subdominant operator is A µ A µ which can condensate in the Landau gauge "vacuum" although being a non-gauge invariant operator. We neglect all higher dimension operators. Then the gluon propagator and the symmetric three gluon vertex only depend on one common unknown condensate. We propose a consistency check from lattice data. At two loops for the leading coefficient and with 1/p 2 corrections at tree-level order the two fitted values for the condensate do not agree. At three loops we argue that the today unknown β MOM 2 should be equal to 1.5(3) × β MOM 2 = 7400(1500) to fulfill the OPE relation. Inclusion of the power corrections' anomalous dimensions should improve further the agreement. We show that these techniques cannot be applied to the asymmetric three gluon vertex with one vanishing momentum. P.A.C

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“…Lattice corrections of order a 2 are negligible compared to statistical and systematic errors. Notice that we have used the standard action, so that we could have easily improved the scaling behaviour by using an improved action [66]- [70] and improved operators.…”

Section: Discussionmentioning

confidence: 99%

Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model

Caracciolo¹,

Montanari²,

Pelissetto³

2000

J. High Energy Phys.

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We consider the short-distance behaviour of the product of the Noether O(N ) currents in the lattice nonlinear σ-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (ma ≈ 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a ∼ < x ∼ < m −1 . We present a detailed discussion of the possible systematic errors.

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Testing the efficiency of different improvement programs

Cited by 5 publications

References 73 publications

Mean-field expansion for spin models with medium-range interactions

Mean-field expansion for spin models with medium-range interactions

Consistent OPE description of gluon two- and three-point Green functions?

Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model

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