Vortices and phase transitions in two-dimensional non-abelian spin models

We modify O(n) models (n>2) in two dimensions so as to comparedifferent thoeries with identical local properties and different global ones. Our O′ (3) model with a particular interaction has vortex-like configuration (π₁(P₂) = Z₂) though it is locally equivalent to an O (3) model (π₁(S₂) = 0). Our results have been obtained by means of strong coupling methods. The Padé extrapolants show a critical value x_c = 11.8.