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

Abstract

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 $m/Ł_\MS = 3.8716$. We use the finite-size scaling method of Lüscher et al. to deduce $m/Ł_\MS$ and find that for the $SO(4)$ model the computed result of $m/Ł_\MS \sim 14$ 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.

27 pages , 1 Postscript-file, uuencoded

References in corpus (8)

• Finite size and temperature effects in the AF Heisenberg model
• New Universality Classes for Two-Dimensional $\sigma$-Models
• O(N) and RP^{N-1} Models in Two Dimensions
• The exact mass-gaps of the principal chiral models
• Possible Failure of Asymptotic Freedom in Two-Dimensional $R{P}^2$ and $R{P}^3$ $\sigma$-Models
• Two dimensional SU(N) x SU(N) chiral models on the lattice
• Radial Excited States for Heavy Quark Systems in NRQCD
• An Improved Estimator for the Correlation Function of 2D Nonlinear Sigma Models

Cited by in corpus (6)

• TBA equations for excited states in the O(3) and O(4) nonlinear $\sigma$-model
• Spin-stiffness and topological defects in two-dimensional frustrated spin systems
• Correction to four-loop RG functions in the two-dimensional lattice O(n) $\sigma$-model
• The nature of the continuum limit in the 2D $R{P}^2$ gauge model
• A determination of the mass gap in the O(n) sigma model
• Double-Scaling Limit in Principal Chiral Model: a New Non-Critical String?