Eur. Phys. J. B 14, 125-137 (2000)
https://doi.org/10.1007/s100510050113

First and second order transition of frustrated Heisenberg spin systems

¹ Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
² Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, 2 avenue A. Chauvin, 95302 Cergy-Pontoise Cedex, France

Received: 17 May 1999
Revised: 30 July 1999
Published online: 15 March 2000

Abstract

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.