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A variable-range interacting Ising model with spin-1/2 particles exhibitsdistinct behavior depending on the fall-off rates in the range of interactions,notably non-local (NL), quasi-local (QL), and local. It is unknown if such atransition occurs in this model with an arbitrary spin quantum number. Weestablish its existence by analyzing the profiles of entanglement entropy,mutual information, and genuine multipartite entanglement (GME) of the weightedgraph state (WGS), which is prepared when the multi-level maximally coherentstate at each site evolves according to the spin-s Ising Hamiltonian.Specifically, we demonstrate that the scaling of time-averaged mutualinformation and the divergence in the first derivative of GME with respect tothe fall-off rate in the WGS can indicate the transition point from NL to QL,which scales logarithmically with individual spin dimension. Additionally, wesuggest that the existence of a saturation value of a finite number of quditscapable of mimicking the GME pattern of an arbitrarily large system-size canreveal the second transition point between quasi-local and local regions.

Revealing Transition in Fall-off Rates of spin-s Ising Model through Multiqudit Graph states