Mass gap of lattice O(3) non-linear sigma-model with naive and improved actions

We evaluate the strong coupling expansion for the mass gap of the euclidean lattice O(3) non-linear sigma-model in two dimensions with the naive action and with the tree level improved action. For the naive action the expansions series exhibits scaling behaviour in the weak coupling region. For the tree level improved action, our series is consistent with Monte Carlo data in the intermediate coupling region but is too short to reproduce the scaling. (orig.)