The weak-coupling phase of lattice spin and gauge models

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We analyze the lattice weak-coupling (w.c.) expansion of O( N), CP N−1 and chiral spin models, and of large- N reduced chiral and gauge models. We find that the w.c. expansion always agrees with mean field results, whenever comparable, for arbitrary space-time dimensions, and that the expansion of the reduced models agrees with that of the original ones. However, w.c. results disagree with one-dimensional large- N and (old and new) exact results. We explain this phenomenon as a failure of the analytic continuation from higher dimensions that defines lattice w.c. perturbation theory for massless models (even if infrared singularities always cancel). We use an improved version of the mean field (m.f.) technique suitable for reduced models. We compute the m.f. approximation of chiral models and use this result to determine the large- d (m.f.) behaviour of reduced gauge models, finding agreement with standard Wilson theory results. We give a new characterization of large- N chiral models in terms of the single-link integral for the adjoint representation of SU( N).