Flat histogram Monte Carlo sampling for mechanical variables and conjugate thermodynamic fields with example applications to strongly correlated electronic systems.

We present a general and unifying framework for deriving Monte Carlo acceptance rules which facilitate flat histogram sampling. The framework yields uniform sampling rules for thermodynamic states given by the mechanically extensive variables appearing in the Hamiltonian. Likewise, Monte Carlo schemes which uniformly sample the thermodynamic fields that are conjugate to the mechanical variables can be derived within this framework. We apply these different, yet equivalent sampling schemes to the extended Hubbard model in the atomic limit with explicit electron spin. Results for the full density-of-states, the charge-order parameter distribution, and phase diagrams for different ratios of the on-site Hubbard repulsion and the intersite interaction are presented. A tricritical point at half-filling of the lattice is located using finite-size scaling techniques.