Noncompact sigma-models: Large N expansion and thermodynamic limit

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dc.creatorDuncan, A.
dc.creatorNiedermaier, M.
dc.creatorWeisz, P.
dc.date2007-06-20
dc.date.accessioned2026-07-07T10:56:18Z
dc.date.available2026-07-07T10:56:18Z
dc.descriptionNoncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d \geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d=2 demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for ``criticality'' and ``triviality'' of the theories in the SO(1,N) invariant sector are discussed.
dc.description46 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0706.2929
dc.identifierhttp://arxiv.org/abs/0706.2929
dc.identifierNucl.Phys.B791:193-230,2008
dc.identifierdoi:10.1016/j.nuclphysb.2007.07.020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186367
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Lattice
dc.titleNoncompact sigma-models: Large N expansion and thermodynamic limit
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