Initial spin fluctuations as a probe of cluster spin structure in ${}^{16}\mathrm{O}$ and ${}^{20}\mathrm{N}\mathrm{e}$ nuclei

We investigate the imprint of $\alpha$ clustering on initial spin fluctuations in relativistic ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and ${}^{20}\mathrm{N}\mathrm{e}+{}^{20}\mathrm{N}\mathrm{e}$ collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.36$~TeV. Utilizing $\mathit{\text{ab}}\mathit{\text{initio}}$ configurations from Nuclear Lattice Effective Field Theory (NLEFT) and phenomenological $\alpha$-cluster models within a Monte-Carlo Glauber framework, we compute the event-by-event variance of the initial net spin polarization. We find that the strong short-range spin–isospin correlations characteristic of $\alpha$ clusters lead to a significant suppression of spin fluctuations compared to a spherical Woods–Saxon baseline with uncorrelated spins. By constructing a scaled fluctuation observable that accounts for trivial finite-size effects, we demonstrate that this suppression exhibits a non-monotonic centrality dependence sensitive to the detailed cluster geometry. Furthermore, we propose the ratio of scaled spin fluctuations between ${}^{20}\mathrm{N}\mathrm{e}$ and ${}^{16}\mathrm{O}$ systems as a robust probe. Our results predict distinct percent-level deviations from the baseline for clustered nuclei, suggesting that measurements of final-state $\mathrm{\Lambda }$-hyperon spin correlations can provide novel constraints on the ground-state spin structure of light nuclei.