  We extend our previous analysis to arbitrary two dimensional SU(N) principal
chiral model in a link formulation. A general expression for the second order
coefficient of fixed distance correlation function is given in terms of Green
functions. This coefficient is calculated for distance 1 and is proven to be
path independent. We also study the weak coupling expansion of the free energy
of one dimensional SU(N) model and explain why it is non-uniform in the volume.
Further, we investigate the contribution of holonomy operators to the
low-temperature expansion in two dimensions. All our results agree with the
conventional expansion. Nevertheless, we give some example which indicates that
the expansion in the link formulation can also suffer from ambiguities
previously found in the conventional perturbation theory.
