Dense Hopfield networks with $p$-body interactions are known for their feature to prototype transition and adversarial robustness. However. theoretical studies have been mostly concerned with their storage capacity. We derive the phase diagram of pattern retrieval in the teacher-student setting of $p$-body networks. https://www.diegojavierfares.com/sale-now-French-Manicure-trade-Panicle-Hydrangea-quick-choice/