Effect of random field disorder on the first order transition in p-spin interaction model

We study the random field p-spin model with Ising spins on a fully connected graph using the theory of large deviations in this paper. This is a good model to study the effect of quenched random field on systems which have a sharp first order transition in the pure state. For p=2, the phase-diagram of the model, for bimodal distribution of the random field, has been well studied and is known to undergo a continuous transition for lower values of the random field (h) and a first order transition beyond a threshold, htp(≈0.439). We find the phase diagram of the model, for all p≥2, with bimodal random field distribution, using large deviation techniques. We also look at the fluctuations in the system by calculating the magnetic susceptibility. For p=2, beyond the tricritical point in the regime of first order transition, we find that for htpho=1/p!), the system does not show ferromagnetic order even at zero temperature. We find that the magnetic susceptibility for p≥3 is discontinuous at the transition point for h