1,858 research outputs found

    On the evaluation of universal non-perturbative constants in O(N) sigma models

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    We investigate the relation between on-shell and zero-momentum non-perturbative quantities entering the parametrization of the two-point Green's function of two-dimensional non-linear O(N) sigma models. We present accurate estimates of ratios of mass-scales and renormalization constants, obtained by an analysis of the strong-coupling expansion of the two-point Green's function. These ratios allow to connect exact known on-shell results with typical zero-momentum lattice evaluations. Our results are supported by the 1/N-expansion.Comment: 10 pages, revte

    Three-Loop Results on the Lattice

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    We present some new three-loop results in lattice gauge theories, for the Free Energy and for the Topological Susceptibility. These results are an outcome of a scheme which we are developing (using a symbolic manipulation language), for the analytic computation of renormalization functions on the lattice.Comment: (Contribution to Lattice-92 conference). 4 page

    Topological susceptibility and string tension in CP(N-1) models

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    We investigate the features of CPN−1{\rm CP}^{N-1} models concerning confinement and topology. In order to study the approach to the large-NN asymptotic regime, we determine the topological susceptibility and the string tension for a wide range of values of NN, in particular N=4,10,21,41N=4,10,21,41. Quantitative agreement with the large-NN predictions is found for the CP20{\rm CP}^{20} and the CP40{\rm CP}^{40} models. Problems related to the measure of the topological susceptibility and the string tension on the lattice are discussed.Comment: Talk presented at the Lattice '92 Conference, Amsterdam. 6 pages, sorry, no figures included, if required we can send them by mai

    Critical behavior of the correlation function of three-dimensional O(N) models in the symmetric phase

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    We present new strong-coupling series for O(N) spin models in three dimensions, on the cubic and diamond lattices. We analyze these series to investigate the two-point Green's function G(x) in the critical region of the symmetric phase. This analysis shows that the low-momentum behavior of G(x) is essentially Gaussian for all N from zero to infinity. This result is also supported by a large-N analysis.Comment: 3 pages, requires espcrc2.st

    Monte Carlo simulation of lattice CPN−1{\rm CP}^{N-1} models at large N

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    In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models. Quantitative agreement with the large-N predictions is found for the correlation length defined by the second moment of the correlation function, the topological susceptibility and the string tension. On the other hand, quantities involving the mass gap are still far from the large-NN results showing a very slow approach to the asymptotic regime. To overcome the problems coming from the severe form of critical slowing down observed at large N in the measurement of the topological susceptibility by using standard local algorithms, we performed our simulations implementing the Simulated Tempering method.Comment: 4 page

    Topological charge on the lattice: a field theoretical view of the geometrical approach

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    We construct sequences of ``field theoretical'' (analytical) lattice topological charge density operators which formally approach geometrical definitions in 2-d CPN−1CP^{N-1} models and 4-d SU(N)SU(N) Yang Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geometrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In perturbation theory renormalization effects formally tend to vanish along such sequences. But, since the perturbative expansion is asymptotic, this does not necessarily lead to well behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormalizations survive.Comment: 14 pages, revte

    Scaling and asymptotic scaling in two-dimensional CPN−1CP^{N-1} models

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    Two-dimensional CPN−1CP^{N-1} models are investigated by Monte Carlo methods on the lattice, for values of NN ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length ξ\xi. Several lattice formulations are compared and shown to enjoy scaling for ξ\xi as small as 2.52.5. Asymptotic scaling is investigated using as bare coupling constant both the usual β\beta and βE\beta_E (related to the internal energy); the latter is shown to improve asymptotic scaling properties. Studies of finite size effects show their NN-dependence to be highly non-trivial, due to the increasing radius of the zˉz\bar z z bound states at large NN.Comment: 5 pages + 12 figures (PostScript), report no. IFUP-TH 46/9

    1/N1/N Expansion of Two-Dimensional Models in the Scaling Region

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    The main technical and conceptual features of the lattice 1/N1/N expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between CPN−1CP^{N-1} and O(2N)O(2N) σ\sigma models, with standard and improved lattice actions. We show how to perform the asymptotic expansion of effective propagators for small values of the mass gap and how to employ this result in the evaluation of physical quantities in the scaling regime. The lattice renormalization group β\beta function is constructed explicitly and exactly to O(1/N)O({1/N}).Comment: 6 pages, report no. IFUP-TH 49/9
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