[10] First and second order transition in frustrated Heisenberg systems

Starting from the hypothesis of a second order transition we have studied modifications of the original Heisenberg antiferromagnet on a stacked triangular lattice (STA--model) by the Monte Carlo technique. The change is a local constraint restricting the spins at the corners of selected triangles to add up to zero without stopping them from moving freely (STAR--model). We have studied also the closely related dihedral and trihedral models which can be classified as Stiefel models. We have found indications of a first order transition for all three modified models instead of a universal critical behavior. This is in accordance with the renormalization group investigations but disagrees with the Monte Carlo simulations of the original STA--model favoring a new universality class. For the corresponding $x$--$y$ antiferromagnet studied before, the second order nature of the transition could also not be confirmed.