Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-23
Nucl.Phys.B788:89-119,2008
Physics
High Energy Physics
High Energy Physics - Theory
37 pages, some corrections made in discussion of the literature
Scientific paper
10.1016/j.nuclphysb.2007.05.028
Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions $d \geq 2$. While the ferro- and antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large $N$ expansions are studied in both types of models and are argued to be asymptotic expansions on a finite lattice. An exact correspondence between the expansion coefficients of the compact and the noncompact models is established, for both expansions, valid to all orders on a finite lattice. The perturbative one involves flipping the sign of the coupling and remains valid in the termwise infinite volume limit. The large $N$ correspondence concerns the functional dependence on the free propagator and holds directly only in finite volume.
Niedermaier Max
Seiler Erhard
Weisz Peter
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