45 research outputs found
Nontrivial fixed point in nonabelian models
We investigate the percolation properties of equatorial strips in the
two-dimensional O(3) nonlinear model. We find convincing evidence that
such strips do not percolate at low temperatures, provided they are
sufficiently narrow. Rigorous arguments show that this implies the vanishing of
the mass gap at low temperature and the absence of asymptotic freedom in the
massive continuum limit. We also give an intuitive explanation of the
transition to a massless phase and, based on it, an estimate of the transition
temperature.Comment: Lattice 2000 (Perturbation Theory
Does Conformal Quantum Field Theory Describe the Continuum Limits of 2D Spin Models with Continuous Symmetry?
It is generally taken for granted that two-dimensional critical phenomena can
be fully classified by the well known two-dimensional (rational) conformal
quantum field theories (CQFTs). In particular it is believed that in models
with a continuous symmetry characterized by a Lie group the continuum
theory enjoys an enhanced symmetry due to the decoupling of right
and left movers. In this letter we review the conventional arguments leading to
this conclusion, point out two gaps and provide a conterexample. Nevertheless
we justify in the end the conventional conclusions by additional arguments.Comment: 9 page
Testing Asymptotic Scaling and Nonabelian Symmetry Enhancement
We determine some points on the finite size scaling curve for the correlation
length in the two dimensional O(3) and icosahedron spin models. The Monte Carlo
data are consistent with the two models possessing the same continuum limit.
The data also suggest that the continuum scaling curve lies above the estimate
of Kim and of Caracciolo et al and thus leads to larger thermodynamic values of
of the correlation length than previously reported.Comment: 10 pages, 3 figures. Some typos corrected and a discussion of recent
work by Caracciolo et al include
Is the 2D O(3) Nonlinear Model Asymptotically Free?
We report the results of a Monte Carlo study of the continuum limit of the
two dimensional O(3) non-linear model. The notable finding is that it
agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix
ansatz and with the continuum limit of the dodecahedron spin model. The latter
finding renders the existence of asymptotic freedom in the O(3) model rather
unlikely.Comment: 10 page
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
Nonlinear -model, form factors and universality
We report the results of a very high statistics Monte Carlo study of the
continuum limit of the two dimensional O(3) non-linear model. We find
a significant discrepancy between the continuum extrapolation of our data and
the form factor prediction of Balog and Niedermaier, inspired by the
Zamolodchikovs' S-matrix ansatz. On the other hand our results for the O(3) and
the dodecahedron model are consistent with our earlier finding that the two
models possess the same continuum limit.Comment: 10 pages, 5 figure