Investigation of possible phase transition of the frustrated spin-1/2 J(1)-J(2)-J(3) model on the square lattice

The frustrated spin-1/2 J (1)-J (2)-J (3) antiferromagnet with exchange anisotropy on the two-dimensional square lattice is investigated. The exchange anisotropy is presented by η with 0 ≤ η < 1. The effects of the J (1), J (2), J (3) and anisotropy on the possible phase transition of the Néel state and collinear state are studied comprehensively. Our results indicate that for J (3) > 0 there are upper limits [Formula: see text] and η (c) values. When 0 < J (3) ≤ [Formula: see text] and 0 ≤ η ≤ η (c), the Néel and collinear states have the same order-disorder transition point at J (2) = J (1)/2. Nevertheless, when the J (3) and η values beyond the upper limits, it is a paramagnetic phase at J (2) = J (1)/2. For J (3) < 0, in the case of 0 ≤ η < 1, the two states always have the same critical temperature as long as J (2) = J (1)/2. Therefore, for J (2) = J (1)/2, under such parameters, a first-order phase transition between the two states for these two cases below the critical temperatures may occur. When J (2) ≠ J (1)/2, the Néel and collinear states may also exist, while they have different critical temperatures. When J (2) > J (1)/2, a first-order phase transition between the two states may also occur. However, for J (2) < J (1)/2, the Néel state is always more stable than the collinear state.