Antiferromagnetic stacked triangular lattices with Heisenberg spins: Phase transition and effect of next-nearest-neighbor interaction

Abstract

We study by extensive histogram Monte Carlo simulations the phase transition in the antiferromagnetic stacked triangular lattices with classical Heisenberg spins. It is shown that in a range of the antiferromagnetic next-nearest-neighbor interaction ${\mathit{J}}_{2}$, the transition is clearly of first order. We also reconsider the controversial question concerning the nature of the phase transition when ${\mathit{J}}_{2}$=0: we show that the critical exponents obtained, in agreement with previous simulations, exclude the possibility of the O(4) class predicted by a nonlinear \ensuremath{\sigma} model in a 2+\ensuremath{\varepsilon} renormalization-group calculation. The phase diagram in the (${\mathit{J}}_{2}$,T) space (T: temperature) is shown and discussed. For comparison, the phase diagram obtained by a Green-function method in the case of quantum Heisenberg spins is also shown.