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We consider the ferromagnetic Ising model with spatially dependent externalfields on a Cayley tree, and we investigate the conditions for the existence ofthe phase transition for a class of external fields, asymptotically approachinga homogeneous critical external field. Our results extend earlier results byRozikov and Ganikhodjaev.

Stability of the Phase Transition of Critical-Field Ising Model on Cayley trees under Inhomogeneous External Fields