Nonlocality of mixtures of the ground and first excited states within $J_{1}-J_{2}$ Heisenberg model.

We investigate both bipartite and multipartite nonlocality in the $J_{1}-J_{2}$ Heisenberg model. Bipartite nonlocality is measured by the CHSH inequality, while multipartite nonlocality is explored through Bell-type inequalities. Our findings reveal that neither ground-state nor full thermal-state nonlocality reliably characterizes quantum phase transitions (QPTs). However, we uncover that the mixed-state nonlocality of the ground and first excited states exhibits distinctive characteristics applicable to both bipartite and multipartite scenarios. We also demonstrate how mixed-state quantum correlation behaviors depend on varying temperature regimes. In the bipartite case, we observe a phenomenon known as "correlation reversal" with increasing temperature, a previously unreported occurrence in other models. For the multipartite case, the ability to signify phase transitions is significantly enhanced as the temperature rises. Furthermore, we discover a linear scaling effect that provides valuable insights for extrapolating QPTs in the thermodynamic limit as $N \rightarrow \infty$. Additionally, we identify the critical temperature at which mixed-state nonlocality becomes a reliable indicator of phase transitions.