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 \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}J 3 cand η c values. When 0 <  J 3  ≤  \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}J 3 cand 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.