Numéro
J. Phys. I France
Volume 6, Numéro 8, August 1996
Page(s) 983 - 992
DOI https://doi.org/10.1051/jp1:1996111
J. Phys. I France 6 (1996) 983-992
DOI: 10.1051/jp1:1996111

On the Large Order Behaviour of the Potts Model

Domenico Maria Carlucci

Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100 Pisa, Italy


Received 8 March 1996, revised 22 April 1996, accepted 2 May 1996

Abstract
Following the work by Houghton, Reeve and Wallace about an alternative formulation of the $n\rightarrow 0$ limit of the (n+1) state Potts model in field theory for the large order behaviour of the perturbative expansion, we generalise their technique to all n by establishing an equivalence in perturbation theory order by order with another bosonic field theory. Restricting ourselves to a cubic interaction, we obtain an explicit expression (in terms of n) for the large order behaviour of the partition function.


Résumé
Suivant le travail de Houghton, Reeve et Wallace concernant une formulation alternative de la limite $n\rightarrow 0$ du modèle de Potts en théorie des champs pour le comportement aux grands ordres, nous généralisons leur technique à n quelconque en établissant une équivalence ordre par ordre en théorie de perturbation avec une autre théorie de champs de bosons. En nous restreignant à une interaction cubique, nous obtenons une expression explicite (en fonction de n) pour le comportement aux grands ordres de la fonction de partition.



© Les Editions de Physique 1996

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