  We study quantum phase transitions of three-dimensional disordered systems in
the chiral classes (AIII and BDI) with and without weak topological indices. We
show that the systems with a nontrivial weak topological index universally
exhibit an emergent thermodynamic phase where wave functions are delocalized
along one spatial direction but exponentially localized in the other two
spatial directions, which we call the quasi-localized phase. Our extensive
numerical study clarifies that the critical exponent of the Anderson transition
between the metallic and quasi-localized phases, as well as that between the
quasi-localized and localized phases, are different from that with no weak
topological index, signaling the new universality classes induced by topology.
The quasi-localized phase and concomitant topological Anderson transition
manifest themselves in the anisotropic transport phenomena of disordered weak
topological insulators and nodal-line semimetals, which exhibit the metallic
behavior in one direction but the insulating behavior in the other directions.
