Institut de Physique Théorique
Direction de la Recherche Fondamentale  -  Saclay
UMR 3681 - INP
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Dimanche 20 août 2017

Publication : t17/131

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Non-scalar operators for the Potts model in arbitrary dimension

Couvreur R. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Jacobsen J.L. ()
Saleur H. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Abstract:
We investigate the operator content of the Q-state Potts model in arbitrary dimension, using the representation theory of the symmetric group. In particular we construct all possible tensors acting on N spins, corresponding to given symmetries under S Q and S N , in terms of representations involving any Young diagram. These operators transform non-trivially under the group of spatial rotations, with a definite conformal spin. The two-point correlation functions are then computed, and their physical interpretation is given in terms of Fortuin-Kasteleyn clusters propagating between two neighbourhoods of each N spins. In two dimensions, we obtain analytically the critical exponent corresponding to each operator. In the simplest and physically most relevant cases, we confirm the values of the critical exponent and the conformal spin by numerical measurements, using both Monte Carlo simulations and transfer matrix diagonalisations. Our classification partially provides the structure of Jordan cells of the dilatation operator in arbitrary dimensions, which in turn gives rise to logarithmic correlation functions.
Année de publication : 2017
Preprint : arXiv:1704.02186
Langue : Anglais

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