Random field Ising model in a random graph

• The nature of the phase transition in the RFIM was investigated, as a function of the connectivity.
• All the simulations were redone, and they are in good agreement with the theory.
• The results confirm that the nature of the transition depends on the random field distribution.

The Random Field Ising Model (RFIM) following bimodal and Gaussian distributions for the RF is investigated using a finite connectivity technique. We focused on determining the order of the phase transition as well as the existence of a tricritical point as a function of the connectivity cc for both types of RF distribution. Our results indicate that for the Gaussian distribution the phase transition is always second-order. For the bimodal distribution, there is indeed a tricritical point. However, its location is strongly dependent on cc. The tricritical point is suppressed below a certain minimum value of connectivity.