The general features of the 1/N expansion in statistical mechanics and quantum held theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the large-N properties of spin and gauge models possessing the symmetry group SU(N)x SU(N). An extensive discussion of the known properties of the single-link integral (equivalent to YM(2) and one-dimensional chiral models) includes finite-N results, the external field solution, properties of the determinant, and the double scaling limit. Two major classes of solvable generalizations are introduced: one-dimensional closed chiral chains and models defined on a d-1 dimensional simplex. In both cases, large-hi solutions are presented with emphasis on their double scaling properties. The available techniques and results concerning unitary-matrix models that correspond to asymptotically free quantum field theories (two-dimensional chiral models and four-dimensional QCD) are discussed, including strong-coupling methods, reduced formulations, and the Monte Carlo approach. (C) 1998 Elsevier Science B.V. All rights reserved.
The large-N expansion of unitary-matrix models
ROSSI, PAOLO;VICARI, ETTORE
1998-01-01
Abstract
The general features of the 1/N expansion in statistical mechanics and quantum held theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the large-N properties of spin and gauge models possessing the symmetry group SU(N)x SU(N). An extensive discussion of the known properties of the single-link integral (equivalent to YM(2) and one-dimensional chiral models) includes finite-N results, the external field solution, properties of the determinant, and the double scaling limit. Two major classes of solvable generalizations are introduced: one-dimensional closed chiral chains and models defined on a d-1 dimensional simplex. In both cases, large-hi solutions are presented with emphasis on their double scaling properties. The available techniques and results concerning unitary-matrix models that correspond to asymptotically free quantum field theories (two-dimensional chiral models and four-dimensional QCD) are discussed, including strong-coupling methods, reduced formulations, and the Monte Carlo approach. (C) 1998 Elsevier Science B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
