  The frustrated isotropic $J_1-J_2$ model with ferromagnetic $J_1$ and
anti-ferromagnetic $J_2$ interactions in presence of an axial magnetic field
shows many exotic phases, such as vector chiral and multipolar phases. The
existing studies of the phase boundaries of these systems are based on the
indirect evidences such as correlation functions {\it etc}. In this paper, the
phase boundaries of these exotic phases are calculated based on order
parameters and jumps in the magnetization. In the strong magnetic field, $Z_2$
symmetry is broken, therefore, order parameter of the vector chiral phase is
calculated using the broken symmetry states. Our results obtained using the
modified density matrix renormalization group and exact diagonalization
methods, suggest that the vector chiral phase exist only in narrow range of
parameter space $J_2/J_1$.
