  We exactly compute the energy density of the integrable O(n) non-linear sigma
model as a convergent series. This series is specifically analysed for the very
important O(6) symmetry, since it was suggested to result as a peculiar limit
of the AdS string theory by Alday and Maldacena [1]. In this respect, the O(6)
model gives also refined confirmations and predictions once compared with the
SYM Bethe Ansatz [2,3].
