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Parisi demonstrated in 1979 that pairwise interactions exhibit a glass spinphase when there is disorder. While he discovered an equilibrium solution ofthe Sherrington-Kirkpatrick (SK) spin-glass model and we know it as acontinuous phase transition, the model dedicated to pairwise interactions andhigher-order interactions has not been addressed. This research intends todetermine whether this phase exists in triplet interactions. Due to theintractable nature of the three interacting spins alone, we employed aperturbation approach to provide an analytical solution for the tripletinteractions in the background of the SK spin-glass model. Our results show theexistence of this phase in the third-order interaction and a sudden transitionthat indicates a change in the nature of a glassy spin system transitioningfrom the continuous order to the first order. It causes a forward shift in thecritical temperature by identifying the frustration of triplet interactions.

Frustration of triplet interaction in spin-glass background