Unveiling the multifaceted properties of square-octagon lattices using the Hubbard model

• The square-octagon lattice is shown to exhibit tunable electronic, magnetic, and thermoelectric properties through variations in physical parameters. • A transition between semiconducting, metallic, and insulating phases is achieved by adjusting the hopping energy and magnetic field. • The study reveals the interplay between temperature, magnetic field, and electron interactions in shaping heat capacity, magnetic susceptibility, and thermal conductivity. • These findings offer valuable insights for designing advanced materials with controllable charge transport and magnetic characteristics. This work explores how the square-octagon lattice (SOL) behaves from electronic, magnetic, thermoelectric, and thermodynamic perspectives. To carry out this investigation, we rely on the Hubbard model combined with the Green’s function approach. The effects of varying second-nearest-neighbor (NN) hopping energy (t 2 ), magnetic field, and on-site Coulomb interaction (OSCI) are systematically explored. By tuning these parameters, we analyze the band structure, density of states (DOS), magnetic susceptibility, electronic heat capacity, thermal conductivity, and Seebeck coefficient (SC). Results show that increasing t 2 reduces the band gap, driving a shift in electronic character from a semiconducting phase to a metallic state. The magnetic field causes energy level splitting and modifies magnetic phases, while the OSCI enhances electron correlation. The heat capacity increases due to electron excitation, while at higher temperatures it decreases, consistent with electronic saturation effects. Magnetic susceptibility reveals transition from paramagnetic to antiferromagnetic behavior with increasing OSCI. Thermal conductivity exhibits a peak at intermediate temperatures, reflecting a balance between carrier excitation and scattering. Additionally, the SC reveals n-type to p-type transitions depending on the Tuning lattice parameters and external fields, enabling control over the physical properties of 2D systems, guiding the design of materials with improved thermoelectric and magnetic performance.