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We present an efficient Monte-Carlo method for long-range interacting systemsto calculate free energy as a function of an order parameter. In this method, avariant of the Wang-Landau method regarding the order parameter is combinedwith the stochastic cutoff method, which has recently been developed forlong-range interacting systems. This method enables us to calculate free energyin long-range interacting systems with reasonable computational time despitethe fact that no approximation is involved. This method is applied to athree-dimensional magnetic dipolar system to measure free energy as a functionof magnetization. By using the present method, we can calculate free energy fora large system size of $16^3$ spins despite the presence of long-range magneticdipolar interactions. We also discuss the merits and demerits of the presentmethod in comparison with the conventional Wang-Landau method in which freeenergy is calculated from the joint density of states of energy and orderparameter.

An Efficient Monte-Carlo Method for Calculating Free-Energy in Long-Range Interacting Systems