The applicability of perturbation expansion to two-dimensional goldstone systems

In the two-dimensional O(n) non-linear σ model, O(n) invariant Green functions are calculated perturbatively with lattice regularization and found to be infrared finite to two loops. This finiteness makes it possible to obtain the correct renormalization group parameters of the theory directly in the symmetric theory without symmetry-breaking terms in the action. It is conjectured that any invariant functional of the fields has an infrared-finite expectation value to any order in the perturbation expansion.