Hysteresis and Criticality in the Bethe-Lattice RFIM with Binary Bond Disorder

We investigate the nonequilibrium random-field Ising model with binary ferromagnetic bond disorder on a Bethe lattice at zero temperature. Using coupled recursion relations and numerical simulations, we study how bond contrast modifies the hysteretic response and critical behaviour of the system. For disorder strengths below the critical disorder of the corresponding uniform-bond model, increasing the bond contrast suppresses the macroscopic avalanche responsible for the discontinuous magnetization jump. The stability of the metastable branch is analyzed through the eigenvalues of the Jacobian matrix of the recursion relations. We determine the phase boundary separating discontinuous and continuous hysteresis regimes and examine the scaling behaviour near the critical disorder region. The analytical results are found to be in excellent agreement with simulations.