Magnetic correlations and superconducting pairing near higher-order Van Hove singularities

We explore magnetic correlations and superconducting pairing near higher-order Van Hove singularities in an extended Hubbard model on honecycomb lattice incorporating third-nearest-neighbor hopping \( t'' \). Using quantum Monte Carlo methods, we identify a crossover between ferromagnetic and antiferromagnetic fluctuations near higher-order Van Hove singularities filling, where \( t'' \) enhances ferromagnetic correlations below while suppressing antiferromagnetic fluctuations toward half-filling. At low doping, \( f_n \)-wave pairing dominates, amplified by higher-order Van Hove singularities-induced divergent density of states. Remarkably, despite general suppression of \( f_n \)-wave pairing by increasing next-nearest neighbor hopping \( t' \) and \( t'' \), a critical \( t'' = 0.15 \) triggers anomalous enhancement via higher-order Van Hove singularities renormalization at a fix $t'$. The nearest-neighbor Coulomb interactions \( V \) suppress superconducting correlation, which exhibiting sign-independent suppression proportional to \( |V| \). These results highlight the interplay of higher-order Van Hove singularities-driven electronic structure, magnetic fluctuations, and pairing symmetry competition in electron correlated systems.