We study correlation effects due to the short-range interactions in the single-wall carbon nanotube. Detailed phase diagrams in weak coupling for (un-)doped nanotubes are obtained and compared to the phases in strong coupling. If the range of the interaction is much larger than the circumference of the nanotube, a new phase arises with the power-law correlations of the kinetic energy across the rungs between different sublattices of the honeycomb. (C) 2002 Elsevier Science B.V. All rights reserved.