Noncompact sigma-models: Large N expansion and thermodynamic limit

Noncompact 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.