Anomaly in the phase diagram of the spin quantum 1/2 anisotropic Heisenberg antiferromagnet model with Dzyaloshinskii-Moriya interaction: A low temperature analysis

We will study phase diagram the quantum spin-1/2 anisotropic Heisenberg antiferromagnet model in the presence of a Dzyaloshinskii-Moriya interaction (D) and a uniform longitudinal (H) magnetic field, where we have observed an anomaly at low temperatures. Using the effective-field theory with a finite cluster N=2 spin (EFT-2) we calculate the phase diagram in the H-D plane on a simple cubic lattice (z=6). We analyzed the cases: anisotropic Heisenberg - case I: (Δ=1), anisotropic Heisenberg - case II: (Δ=0.5) and anisotropic Heisenberg - case III: (Δ=0), where only second order phase transitions are observed.