98 research outputs found
Questionable Arguments for the Correctness of Perturbation Theory in Non-Abelian Models
We analyze the arguments put forward recently by Niedermayer et al in favor
of the correctness of conventional perturbation theory in non-Abelian models
and supposedly showing that our super-instanton counterexample was sick. We
point out that within their own set of assumptions, the proof of Niedermayer et
al regarding the correctness of perturbation theory is incorrect and provide a
correct proof under more restrictive assumptions. We reply also to their claim
that the S-matrix bootstrap approach of Balog et al supports the existence of
asymptotic freedom in the O(3) model.Comment: 9 page
Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
We study the universality between a discrete spin model with icosahedral
symmetry and the O(3) model in two dimensions. For this purpose we study
numerically the renormalized two-point functions of the spin field and the four
point coupling constant. We find that those quantities seem to have the same
continuum limits in the two models. This has far reaching consequences, because
the icosahedron model is not asymptotically free in the sense that the coupling
constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in
the short distance limit. By universality this then also applies to the O(3)
model, contrary to the predictions of perturbation theory.Comment: 18 pages, 8 figures Color coding in Fig. 5 changed to improve
visibilit
Comment on "Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models"
In a recent letter (hep-lat/9311019) A. Patrascioiu and E. Seiler argued that
when taking into account "superinstantons configurations" the perturbative
expansion and the beta-function of the two-dimensional non-linear sigma-model
are modified at two loops order. I point out that: (1) perturbation theory in a
superinstanton background is infra-red singular beyond three loops; (2) the new
infra-red singular terms, which change the two loop terms, come from singular
operators - describing superinstanton insertions - in the OPE; (3) taking into
account these operators, the beta-function is not modified. Therefore the
results of Patrascioiu and Seiler do not contradict perturbation theory.Comment: 1 page, REVTeX, no figure
Quasi-asymptotic freedom in the two dimensional O(3) model
The behaviour of the renormalized spin 2-point function in the O(3) and
dodecahedron spin model are investigated numerically. The Monte Carlo data show
excellent agreement between the two models. The short distance behavior comes
very close to standard theoretical expectations, yet it differs significantly
from it. A possible explanation of this situation is offered.Comment: 4 pages, 4 figure
Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit
We discuss some aspects of the continuum limit of some lattice models, in
particular the models. The continuum limit is taken either in an
infinite volume or in a box whose size is a fixed fraction of the infinite
volume correlation length. We point out that in this limit the fluctuations of
the lattice variables must be and thus restore the symmetry which may
have been broken by the boundary conditions (b.c.). This is true in particular
for the so-called super-instanton b.c. introduced earlier by us. This
observation leads to a criterion to assess how close a certain lattice
simulation is to the continuum limit and can be applied to uncover the true
lattice artefacts, present even in the so-called 'perfect actions'. It also
shows that David's recent claim that super-instanton b.c. require a different
renormalization must either be incorrect or an artefact of perturbation theory.Comment: 14 pages, latex, no figure
Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models
In dimension the low temperature behavior of systems enjoying a
continuous symmetry is dominated by super-instantons: classical configurations
of arbitrarily low energy. Perturbation theory in the background of a
super-instanton produces thermodynamic answers for the invariant Green's
functions that differ from the standard ones, but only in non-Abelian models
and only starting at . This effect modifies the -function
of the models and persists in the large limit of the models.Comment: 8 pages, plain LaTeX, MPI-Ph/93-87 and AZPH-TH/93-3
Lattice artefacts and the running of the coupling constant
We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in
the two dimensional O(3) nonlinear model. To investigate the continuum
limit we refine the lattice spacing from the value used by LWW up
to . We find that the lattice artefacts are much larger than
estimated by LWW and that most likely the coupling constant runs slower than
predicted by perturbation theory. A precise determination of the running in the
continuum limit would require a controlled ansatz of extrapolation, which, we
argue, is not presently available.Comment: 4 pages, 4 figures. To address the criticism that we are studying a
different quantitiy than Luscher, Weisz and Wolff originally did, we
introduced a new equation (2), a new paragraph discussing this issue and a
new figure comparing the results obtained with our prescription to that
obtained with the original one of Luscher, Weisz and Wolf
- âŠ