Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function

Abstract

Analytical and numerical methods are applied to principal chiral models on a two-dimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of SU(N) models are developed and applied to the evaluation of the two-point correlation function. The momentum-space lattice propagator is constructed with precision O(β^{10}) and an evaluation of the correlation length is obtained for several different definitions. Three-loop weak coupling contributions to the internal energy and to the lattice $\beta$ and $\gamma$ functions are evaluated for all N, and the effect of adopting the ``energy'' definition of temperature is computed with the same precision. Renormalization-group improved predictions for the two-point Green's function in the weak coupling ( continuum ) regime are obtained and successfully compared with Monte Carlo data. We find that strong coupling is predictive up to a point where asymptotic scaling in the energy scheme is observed. Continuum physics is insensitive to the effects of the large N phase transition occurring in the lattice model. Universality in N is already well established for $N\ge 10$ and the large N physics is well described by a ``hadronization'' picture.

Revtex, 37 pages, 16 figures available on request by FAX or mail

References in corpus (2)

• Topological susceptibility and string tension in the lattice CP(N) models
• Two dimensional SU(N) x SU(N) chiral models on the lattice

Cited by in corpus (16)

• Spectrum of confining strings in SU(N) gauge theories
• Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at correlation length $4\times 10^5$
• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• Large-N phase transition in lattice 2-d principal chiral models
• A strong-coupling analysis of two-dimensional O(N) sigma models with $N\ge 3$ on square, triangular and honeycomb lattices
• Strong-coupling expansion of chiral models
• Twisted Eguchi-Kawai Reduced Chiral Models
• Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory
• Strong coupling analysis of the large-N 2-d lattice chiral models
• Nontrivial Thermodynamics in 't Hooft's Large-$N$ Limit
• The universal coefficient of the exact correlator of a large-$N$ matrix field theory
• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• Hybrid Monte Carlo Simulation with Fourier Acceleration of the $N=2$ Principal Chiral Model in two Dimensions
• Strong coupling expansion of chiral models
• An Approximate Large $N$ Method for Lattice Chiral Models
• Confinement-Higgs Phase Crossover as a Lattice Artifact in 1+1 Dimensions