The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A   variational method study
  The phase transition of the quantum spin-1/2 frustrated Heisenberg antiferroferromagnet on an anisotropic square lattice is studied by using a variational treatment. The model is described by the Heisenberg Hamiltonian with two antiferromagnetic interactions: nearest-neighbor (NN) with different coupling strengths J_{1} and J_{1'} along x and y directions competing with a next-nearest-neighbor coupling J_{2} (NNN). The ground state phase diagram in the ({\lambda},{\alpha}) space, where {\lambda}=J_{1'}/J_{1} and {\alpha}=J_{2}/J_{1}, is obtained. Depending on the values of {\lambda} and {\alpha}, we obtain three different states: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate region {\lambda}_{1}<{\lambda}<1 we observe a QP state between the ordered AF and CAF phases, which disappears for {\lambda} above some critical value {\lambda}_{1}. The boundaries between these ordered phases merge at the quantum critical endpoint (QCE). Below this QCE there is again a direct first-order transition between the AF and CAF phases, with a behavior approximately described by the classical line {\alpha}_{c}{\simeq}{\lambda}/2. 
Orlando D. Mabelini, Octavio Salmon, and J. Ricardo de Sousa
cond-mat.stat-mech cond-mat.str-el