A Rigorous Statistical Mechanical Treatment of Phase Transitions in Strongly Correlated Electron Systems in Nigerian Ore Minerals

Strongly correlated electron systems, in which quantum mechanical interactions between electrons fundamentally alter material properties relative to independent-electron predictions, exhibit remarkable phenomena including metal-insulator transitions, unconventional superconductivity, and orbital ordering. Several ore minerals of economic interest in Nigeria, including magnetite, ilmenite, and chromite found in Ogun, Edo, and Plateau states, are strongly correlated electron systems whose phase transition behaviour is incompletely understood. This study develops a rigorous statistical mechanical treatment of phase transitions in these minerals using dynamical mean field theory extended to multi-orbital Hubbard Hamiltonians. The DMFT equations are solved using the continuous-time quantum Monte Carlo method implemented in the TRIQS software package. Electronic structure inputs including crystal field parameters and Slater integrals are derived from relativistic DFT+U calculations. Temperature-dependent resistivity, magnetic susceptibility, and optical conductivity are computed and compared with measurements on single crystal specimens extracted from Nigerian ore deposits and characterised at the National Metallurgical Development Centre in Jos. Results demonstrate that magnetite's Verwey transition at 120 K is driven by charge ordering on the octahedral iron sites, with a predicted transition temperature within 8 K of the measured value. Keywords: strongly correlated electrons, dynamical mean field theory, phase transition, magnetite, Nigeria ore minerals