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

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 J₂, the transition is clearly of first order. We also reconsider the controversial question concerning the nature of the phase transition when J₂=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 {σ} model in a 2+{ε} renormalization-group calculation. The phase diagram in the (J₂,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.