  We study many-body phase transitions in a one-dimensional ferromagnetic
transversed field Ising model with an imaginary field and show that the system
exhibits three phase transitions: one second-order phase transition and two
$\mathcal{PT}$ phase transitions. The second-order phase transition occurring
in the ground state is investigated via biorthogonal and self-normal
entanglement entropy, for which we develop an approach to perform finite-size
scaling theory to extract the central charge for small systems. Compared with
the second-order phase transition, the first $\mathcal{PT}$ transition is
characterized by the appearance of an exceptional point in the full energy
spectrum, while the second $\mathcal{PT}$ transition only occurs in specific
excited states. Furthermore, we interestingly show that both of exceptional
points are second-order in terms of scalings of imaginary parts of the energy.
This work provides an exact solution for many-body phase transitions in
non-Hermitian systems.
