LAUSR

We study a p-spin model with ferromagnetic coupling and quenched random crystal fields for p≥3 for spin-1 systems. We find that the model has lines of first-order transitions at finite temperature (T) for all p≥3. For bimodal distribution of the random crystal field these lines meet at a triple point for weak strength of the crystal field (Δ). Beyond a critical strength of Δ, they do not meet and one of the lines ends at a critical point (T_{c}). Interestingly, we find that on increasing T from T_{c}, keeping other parameters fixed, the system undergoes one more transition which is first order in its character. The system thus exhibits a Gardner-like transition for a range of parameters for all finite p≥3. For p→∞ the model behaves differently and there is only one random first-order transition at T=0.