Phase transitions in 2D $J_{1}-J_{2}$ model with arbitrary signs of exchange interactions

The ground state of the $S=1/2$ $J_{1}-J_{1}$ Heisenberg model on the 2D square lattice with arbitrary signs of exchange constants is considered. States with different spin long-range order types (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as disordered spin-liquid states are described in the frames of one and the same analytical approach. It is shown inter alia, that the phase transition between ferromagnetic spin liquid and long-range order ferromagnet is a second-order one. On the ordered side of the transition the ferromagnetic state with rapidly varying condensate function is detected.

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