a b s t r a c tWe study, using a self-consistent harmonic approximation, the quasi-two-dimensional frustrated Heisenberg antiferromagnet with easy-plane single ion anisotropy. Besides the transition temperature from the high-temperature paramagnetic phase to the low-temperature ordered phase, we also obtain, at zero temperature, the critical single ion anisotropy parameter D c that separates the low D region from the large D quantum paramagnetic phase. We have found disordered phases at zero temperature that could be possible candidates for spin liquids states.

We have studied the ground state phase diagram of the quantum spin-1/2 frustrated Heisenberg antiferromagnet on a square lattice by using the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory for a cluster with two spins (EFT-2). The model is described using the Heisenberg Hamiltonian with two competing antiferromagnetic interactions: nearest neighbor (NN) with different coupling strengths J 1 and J 1 along the x and y directions and next nearest neighbor (NNN) with coupling J 2 . We propose a functional for the free energy (similar to the Landau expansion) and using Maxwell construction we obtain the phase diagram in the (λ, α) space, where λ = J 1 /J 1 and α = J 2 /J 1 . We obtain three different states depending on the values of λ and α: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate

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