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

Alles, B.; Buonanno, A.; Cella, G.

doi:10.1016/S0550-3213(97)00350-7

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

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Buonanno, A.
Dipartimento di Fisica dell'Università and INFN;
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0019-BE1D-A

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.