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キーワード:
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
要旨:
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.
