Phase transitions in the 2D $J_1$–$J_2$ Heisenberg model with arbitrary signs of exchange interactions

The ground state of the $J_1$–$J_2$ Heisenberg model with arbitrary signs of exchange is studied for spin $S = 1/2$ in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.