Configurational free energy in order-disorder transitions from Monte Carlo calculations for systems under external fields

A procedure for calculating the configurational free energy with the Monte Carlo simulation is presented, accounting for the case of the application of external fields. First, the free energy for the L₁₀ ordering systems without any external fields has been evaluated for the various values of the second nearest-neighbor effective interaction, and the feature of this method has been discussed from the viewpoint of the pair correlation. Next, this method has been applied to the case of application of external fields, demonstrating the calculation of the free energy under an external stress field for the L₁₀ phase that has a tetragonal distortion dependent on the long-range order parameter.