Parisi demonstrated in 1979 that pairwise interactions exhibit a glass spin
phase when there is disorder. While he discovered an equilibrium solution of
the Sherrington-Kirkpatrick (SK) spin-glass model and we know it as a
continuous phase transition, the model dedicated to pairwise interactions and
higher-order interactions has not been addressed. This research intends to
determine whether this phase exists in triplet interactions. Due to the
intractable nature of the three interacting spins alone, we employed a
perturbation approach to provide an analytical solution for the triplet
interactions in the background of the SK spin-glass model. Our results show the
existence of this phase in the third-order interaction and a sudden transition
that indicates a change in the nature of a glassy spin system transitioning
from the continuous order to the first order. It causes a forward shift in the
critical temperature by identifying the frustration of triplet interactions.Comment: 6 pages, 2 figure