  Recently, the search for an axion insulator state in the ferromagnet-3D
topological insulator (TI) heterostructure and $\mathrm{MnBi_2Te_4}$ has
attracted intensive interest. However, its detection remains difficult in
experiments. We systematically investigate the disorder-induced phase
transition of the axion insulator state in a 3D TI with antiparallel
magnetization alignment surfaces. It is found that there exists a 2D
disorder-induced phase transition which shares the same universality class with
the quantum Hall plateau to plateau transition. Then, we provide a
phenomenological theory which maps the random mass Dirac Hamiltonian of the
axion insulator state into the Chalker-Coddington network model. Therefore, we
propose to probe the axion insulator state by investigating the universal
signature of such a phase transition in the ferromagnet-3D TI heterostructure
and $\mathrm{MnBi_2Te_4}$. Our findings not only show a global phase diagram of
the axion insulator state, but also provide a new experimental routine to probe
it.
