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(beta10) 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 greater than or similar to 10 and the large N physics is well described by a ''hadronization'' picture.
2-DIMENSIONAL SU(N)XSU(N) CHIRAL MODELS ON THE LATTICE .2. THE GREEN-FUNCTION
ROSSI, PAOLO;VICARI, ETTORE
1994-01-01
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(beta10) 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 greater than or similar to 10 and the large N physics is well described by a ''hadronization'' picture.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
