Zero Temperature Hysteresis in Random Field Ising Model on Bethe Lattices: approach to mean field behavior with increasing coordination number z

We consider the analytic solution of the zero temperature hysteresis in the random field Ising model on a Bethe lattice of coordination number $z$, and study how it approaches the mean field solution in the limit z-> \infty. New analytical results concerning the energy of the system along the hysteresis loop and first order reversal curves (FORC diagrams) are also presented.