The spin-1 two-dimensional J1-J2 Heisenberg antiferromagnet on a triangular lattice

The spin-1 Heisenberg antiferromagnet on a triangular lattice with the nearest- and next-nearest-neighbor couplings, J1=(1−p)J and J2=pJ, J>0, is studied in the entire range of the parameter p. Mori's projection operator technique is used as a method which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature four second-order phase transitions are observed. At p≈0.038 the ground state is transformed from the long-range ordered 120° spin structure into a state with short-range ordering, which in its turn is changed to a long-range ordered state with the ordering vector Q′=(0,−2π3) at p≈0.2. For p≈0.5 a new transition to a state with a short-range order occurs. This state has a large correlation length which continuously grows with p until the establishment of a long-range order happens at p≈0.65. In the range 0.5