Stability of the Phase Transition of Critical-Field Ising Model on   Cayley trees under Inhomogeneous External Fields
  We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev. 
Rodrigo Bissacot, Eric Ossami Endo and Aernout C. D. van Enter
math-ph cond-mat.stat-mech math.MP math.PR