Improved methods for calculating thermodynamic properties of magnetic systems using Wang-Landau density of states

The Wang-Landau method [F. Wang and D. P. Landau, Phys. Rev. E 64, 056101 (2001)] is an efficient way to calculate the density of states (DOS) for magnetic systems, and the DOS can then be used to rapidly calculate the thermodynamic properties of the system. A technique is presented that uses the DOS for a simple Hamiltonian to create a stratified sample of configurations which are then used calculate a warped'' DOS for more realistic Hamiltonians. This technique is validated for classical models of bcc Fe with exchange interactions of increasing range, but its real value is using the DOS for a model Hamiltonian calculated on a workstation to select the stratified set of configurations whose energies can then be calculated for a density-functional Hamiltonian. The result is an efficient first-principles calculation of thermodynamic properties such as the specific heat and magnetic susceptibility. Another technique uses the sample configurations to calculate the parameters of a model exchange interaction using a least-squares approach. The thermodynamic properties can be subsequently evaluated using traditional Monte Carlo techniques for the model exchange interaction. Finally, a technique that uses the configurations to train a neural network to estimate the configuration energy is also discussed. This technique could potentially be useful in identifying the configurations most important in calculating the warped'' DOS.