We demonstrate that random flux is able to drive nontrivial topological phase transitions, in particular between weak topological insulators (WTIs) and Chern insulators (CIs), illustrated on an anisotropic Wilson-Dirac model in two dimensions. Remarkably, an intriguing topological transition sequence $\mathrm{WTIs}\to \mathrm{CIs}\to \mathrm{WTIs}$ occurs with the reentrance to a WTI but of different weak topology, which is unattainable with chemical potential disorder. The involvement of anisotropy and weak topology in such a transition gives rise to emergent quasicritical points, where eigen states are extended in one spatial direction but localized in the other one. This new quantum criticality lies outside the conventional quantum Hall universality class. We provide a comprehensive characterization of the random-flux-induced phase transitions and quantum criticality from both bulk and boundary perspectives. Our results describe a qualitatively new disorder effect based on the interplay of random flux with topological phases of matter.

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• Topological phase transition
• Topological phases of matter
• Disordered systems
• Topological materials
• Discrete symmetries in condensed matter
• Green's function methods