<p>Multipartite nonlocality, a phenomenon in many-body quantum systems which cannot be explained by any local realistic theory, can be witnessed using Bell-type inequalities and Mermin–Klyshko–Svetlichny (MKS) operators. While numerical optimizations are commonly employed in this context, they leave several important questions unresolved. For instance, an intuitive physical understanding of the optimal MKS operators remains elusive. In this paper, we derive analytical solutions for ground-state multipartite nonlocality in a cluster-Ising model. The analytical solutions help us to improve the transfer matrix theory of nonlocality and provide a deep insight into the nature of MKS operators by connecting them to string-order operators composed of standard Pauli operators (e.g., <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hat{\sigma }^x\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mover accent="true"> <mi>σ</mi> <mo stretchy="false">^</mo> </mover> <mi>x</mi> </msup> </math></EquationSource> </InlineEquation>) and spin ladder operators (e.g., <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\hat{S}^{\pm }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mover accent="true"> <mi>S</mi> <mo stretchy="false">^</mo> </mover> <mo>±</mo> </msup> </math></EquationSource> </InlineEquation>). The findings pave the way for both theoretical advancements and experimental applications.</p>