Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$

Details Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$ Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$

1995-11-02

arxiv.org/abs/hep-lat/9511004v1

Phys.Rev. D53 (1996) 5075-5089

Physics

High Energy Physics

High Energy Physics - Lattice

27 pages , 1 Postscript-file, uuencoded

Scientific paper

10.1103/PhysRevD.53.5075

We investigate the continuum limit in $SO(N)$ Principal Chiral Models concentrating in detail on the $SO(4)$ model and its covering group SU(2)xSU(2). We compute the mass gap in terms of Lambda_MS and compare with the prediction of Hollowood of $m/\L_\MS = 3.8716$. We use the finite-size scaling method of L\"uscher et al. to deduce $m/\L_\MS$ and find that for the $SO(4)$ model the computed result of $m/\L_\MS \sim 14$ is in strong disagreement with theory but that a similar analysis of the SU(2)xSU(2) yields excellent agreement with theory. We conjecture that for $SO(4)$ violations of the finite-size scaling assumption are severe forthe values of the correlation length, $\xi$, investigated and that our attempts to extrapolate the results to zero lattice spacing, although plausible, are erroneous. Conversely, the finite-size scaling violations in the SU(2)xSU(2) simulation are consistent with perturbation theory and the computed $beta-$function agrees well with the 3-loop approximation for couplings evaluated at scales $L/a \le \xi$, where $\xi$ is measured in units of the lattice spacing, $a$. We conjecture that lattice vortex artifacts in the $SO(4)$ model are responsible for delaying the onset of the continuum limit until much larger correlation lengths are achieved notwithstanding the apparent onset of scaling. Results for the mass spectrum for SO(N) m, N=8,10 are given whose comparison with theory gives plausible support to our ideas.

Affiliated with

Also associated with

No associations

Rating

Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-299405