[14] Phase transitions in generalized chiral or Stiefel's models

We study by Monte Carlo simulations the phase transition in generalized chiral or Stiefel's models. These models are characterized by a breakdown of symmetry $O(N)/O(N-P)$. We show that for $P=N$ and $P=N-1$ the phase transition is clearly of first order for $N \ge 3$ contrary to predictions based on the Renormalization Group in $4-\epsilon$ expansion.