Pairing phase favored by magnetic frustration.

The interplay between magnetic frustration and pairing is investigated by adopting a BCS-like pairing mechanism on the frustrated $J_1-J_2$ Ising model on the square lattice. The ground-state and thermal phase transitions of the model are analyzed using a fermionic formulation within a cluster mean-field method. In this approach, the lattice system is divided into identical clusters, where the intracluster dynamic is exactly solved, and the intercluster interactions are replaced by self-consistent mean fields. We introduce a framework with two pairing couplings: an intracluster local coupling, $g$, which controls the electron pairing and its mobility within the clusters, and an intercluster coupling, $g'$, which adjusts the pairing mechanism between clusters. Tuning $g'/g$ allows evaluating how the pairing phase evolves from a weak pairing coupling between clusters (clustered system) to a strong one ($g' \rightarrow g$, homogeneous system). In the range $0 \le g'/g \le 1$, we find that a gradual increase in $g'/g$ favors the pairing phase and induces a change in criticality. In particular, our results reveal the presence of tricriticality for a certain range of $g'/g$. In addition, an increase in competing magnetic interactions weakens the magnetic orders, causing the pairing phase to occur at lower strengths of pairing interactions, especially when $g' = g$. Therefore, our findings support that magnetic frustration favors the pairing phase, contributing to the onset of a superconducting state.