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  Perturbation theory predictions and Monte Carlo simulations for the 2-d O(n) non-linear sigma-model

Alles, B., Buonanno, A., & Cella, G. (1997). Perturbation theory predictions and Monte Carlo simulations for the 2-d O(n) non-linear sigma-model. Nuclear Physics B, 500, 513-543. doi:10.1016/S0550-3213(97)00350-7.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0019-BE1D-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0019-BE24-5
Genre: Journal Article

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Alles, B., Author
Buonanno, A.1, 2, Author              
Cella, G., Author
Affiliations:
1Dipartimento di Fisica dell'Università and INFN, ou_persistent22              
2Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1933290              

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Free keywords: High Energy Physics - Lattice, hep-lat,comp-gas, Condensed Matter, cond-mat,High Energy Physics - Theory, hep-th,Nonlinear Sciences, Cellular Automata and Lattice Gases, nlin.CG,Nonlinear Sciences, Exactly Solvable and Integrable Systems, nlin.SI,solv-int
 Abstract: By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough lattices to have a good control on finite-size effects. The magnetic susceptibility and three different definitions of the correlation length are measured. We check our results with large-n expansions as well as with standard formulae for asymptotic freedom up to 4 loops in the standard and effective schemes. For this purpose the weak coupling expansions of the energy up to 4 loops for the standard action and up to 3 loops for the Symanzik action are calculated. For the O(3) model we have used two different effective schemes and checked that they lead to compatible results. A great improvement in the results is obtained by using the effective scheme based on the energy at 3 and 4 loops. We find that the O(8) model follows very nicely (within few per mille) the perturbative predictions. For the O(3) model an acceptable agreement (within few per cent) is found.

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 Dates: 1997-01-071997-01-281997
 Publication Status: Published in print
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 Rev. Method: -
 Identifiers: arXiv: hep-lat/9701001
DOI: 10.1016/S0550-3213(97)00350-7
URI: http://arxiv.org/abs/hep-lat/9701001
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Title: Nuclear Physics B
Source Genre: Journal
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Publ. Info: Amsterdam : North-Holland
Pages: - Volume / Issue: 500 Sequence Number: - Start / End Page: 513 - 543 Identifier: ISSN: 0550-3213
CoNE: /journals/resource/954925564667