Cluster mean-field theory study of J1-J2 Heisenberg model on a square lattice.

We study the spin-1/2 J1-J2 Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size L to infinity, we obtain accurate phase boundaries J(c1)(2) ≈ 0.42 (between the Néel antiferromagnetic phase and non-magnetic phase), and J(c2)(2) ≈ 0.59 (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at J(c1)(2) and the first-order one at J(c2)(2). For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.