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Purpose of this paper is to face up to P-spin glass and Gaussian P-spinmodel, i.e. spin glasses with polynomial interactions of degree P > 2. Weconsider the replica symmetry and first step of replica simmetry breakingassumptions and we solve the models via transport equation and Guerra'sinterpolating technique, showing that we reach the same results. \\ Thus, usingrigorous approaches, we recover the same expression for quenched statisticalpressure and self-consistency equation in both assumption found with othertechniques, including the well-known \textit{replica trick} technique. \\ Atthe end, we show that for $P=2$ the Gaussian P-spin glass model isintrinsecally RS.

Rigorous approaches for spin glass and Gaussian spin glass with P-wise interactions