Exact calculation of the energy contributions to the T=0 random-field   Ising model with metastable dynamics on the Bethe lattice
  We analyze the energy terms corresponding to the spin-spin exchange and spin-random field coupling of the zero temperature random-field Ising model on the Bethe lattice driven by an external field with metastable dynamics. Exact results are calculated as a function of the standard deviation of the disorder and the coordination number z, and compared with numerical simulations on random graphs for z=4, for which a disorder-induced transition takes place. 
Xavier Illa, Jordi Ortin and Eduard Vives