Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

The frustrated spin-1/2 J1a-J1b-J2 antiforrornagnet with anisotropy on the two-diinonsional square lattice was investigated,where the parameters J1a and Ju,represent the nearest neighbor exchanges and along the x and y directions,respectively.J2 represents the next-nearest neighbor exchange.The anisotropy includes the spatial and exchange anisotropies.Using the double-time Green’s function method,the offects of the interplay of exchanges and anisotropy on the possible phase transition of the Neel state and stripe state were discussed.Our results indicated that,in the case of anisotropic parameter 0 ≤η< 1,the Neel and stripe states can exist and have the same critical temperature as long as J2 =J1b/2.Under such parameters,a first-order plia.se transformation between the Neel and stripe states can occur below the critical point.For J2≠J1b/2,our results indicate that the Neel and stripe states can also exist,while their critical temperatures differ.When J2 >J1b/2,a first-order phase transformation between the two states may also occur.However,for J2 < J1b/2,the Neel state is always more stable than the stripe state.

Phase transition of the frustrated antiferromagntic J1-J2-J3 spin-1/2 Heisenberg model on a simple cubic lattice

We have comprehensively investigated the frustrated J1-J2-J3 Heisenberg model on a simple cubic lattice. This model allows three regimes of magnetic order, viz., (π;π;π), (0;π;π) and (0;0;π), denoted as AF1, AF2, and AF3, respectively. The effects of the interplay of neighboring couplings on the model are studied in the entire temperature range. The zero temperature magnetic properties of this model are discussed utilizing the linear spin wave (LSW) theory, nonlinear spin wave (NLSW) theory, and Green’s function (GF) method. The zero temperature phase diagrams evaluated by the LSW and NLSW methods are illustrated, and are observed to exhibit different parameter boundaries. In certain regions and along the parameter boundaries, the possible phase transformations driven by the parameters are discussed. The results obtained using the LSW, NLSW, and GF methods are compared with those obtained using the series expansion (SE) method, and are observed to be in good agreement when the value of J2 is not close to the parameter boundaries. The ground state energies obtained using the LSW and NLSW methods are close to that obtained using the SE method. At finite temperatures, only the GF method is employed to evaluate the magnetic properties, and the calculated phase diagram is observed to be identical to the classical phase diagram. The results indicate that at the parameter boundaries, a temperature-driven first-order phase transition between AF1 and AF2 may occur along the boundary line. Along the AF1-AF3 and AF2-AF3 boundary lines, AF3 is less stable than AF1 and AF2. Our calculated critical temperature agrees with that obtained using Monte Carlo simulations and pseudofermion functional renormalization group scheme.