Ifup-th 56/96
نویسندگان
چکیده
The two-phase issue in the O(n) non-linear σ-model: a Monte-Carlo study Our paper [1] has motivated a comment [2] by A. Patrascioiu and E. Seiler which we reply in this note. The remarks in [2] concern three statements that the authors select from our paper: i) " The results for O(8) support the asymptotic freedom scenario ". The authors in [2] argue that at small˜β ≡ β/8 the O(8) is expected to behave like the spherical model. This conclusion is based on the Borel summability of the 1/N expansion at small˜β [3]. No rigorous proof has been given concerning the behaviour of the series at large˜β. In [2] it is not shown if our working β's (β ∼ 4.6 − 6.5) lie in the " small " or " large " ˜ β region but at least we can say that if the results from our Monte Carlo data fit so nicely the P T predictions for the O(8) model (within few per mille for the mass gap and susceptibility predictions, see [4]) there is reasonable room to think that the exact O(8) model (what we simulate) has a critical point at g = 0 and the set of P T predictions are correct. If our data had to agree only with the spherical model then the small difference between our result for the mass gap and the P. Hasenfratz et al. [5] prediction, 0.5% (compared to the difference of almost 30% between the n = 8 and the n = ∞ predictions) would become an intriguing challenge. Considering it as an accident is a matter of feelings.
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