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The large-N expansion of unitary-matrix models

Rossi, Paolo and Campostrini, Massimo and Vicari, Ettore (1998) The large-N expansion of unitary-matrix models. Physics Reports, 302 . p. 143. ISSN 1873-6270

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The general features of the 1/N expansion in statistical mechanics and quantum field 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 $SU(N) \times SU(N)$. 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-N 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.

Item Type: Article
Additional Information: Imported from arXiv
Subjects: Area02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici
Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI FISICA " E. FERMI"
Depositing User: dott.ssa Sandra Faita
Date Deposited: 09 Apr 2015 15:55
Last Modified: 09 Apr 2015 15:55
URI: http://eprints.adm.unipi.it/id/eprint/1826

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