Investigation of possible phase transition of the frustrated spin-1/2 J1-J2-J3 model on the square lattice

The frustrated spin-1/2 J1-J2-J3 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 J1, J2, J3 and anisotropy on the possible phase transition of the Néel state and collinear state are studied comprehensively. Our results indicate that for J3 > 0 there are upper limits J3c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{3}^{c}$$\end{document} and ηc values. When 0 < J3 ≤ J3c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{3}^{c}$$\end{document} and 0 ≤ η ≤ ηc, the Néel and collinear states have the same order-disorder transition point at J2 = J1/2. Nevertheless, when the J3 and η values beyond the upper limits, it is a paramagnetic phase at J2 = J1/2. For J3 < 0, in the case of 0 ≤ η < 1, the two states always have the same critical temperature as long as J2 = J1/2. Therefore, for J2 = J1/2, under such parameters, a first-order phase transition between the two states for these two cases below the critical temperatures may occur. When J2 ≠ J1/2, the Néel and collinear states may also exist, while they have different critical temperatures. When J2 > J1/2, a first-order phase transition between the two states may also occur. However, for J2 < J1/2, the Néel state is always more stable than the collinear state.