The CrMES scheme as an alternative to Importance Sampling: The tail regime of the order-parameter distribution

We review the recently developed critical minimum energy-subspace (CrMES) technique. This scheme produces an immense optimization of popular algorithms, such as the Wang-Landau (WL) and broad histogram methods, by predicting the essential part of the energy space necessary for the estimation of the critical behavior and provides a new route of critical exponent estimation. A powerful and efficient CrMES entropic sampling scheme is proposed as an alternative to the traditional importance sampling methods. Utilizing the WL random walk process in the dominant energy subspace (CrMES-WL sampling) and using the WL approximation of the density of states and appropriate microcanonical estimators we determine the magnetic properties of the 2D Ising model. Updating $(E,M)$ histograms during the high level WL-iterations, we provide a comprehensive alternative scheme to the Metropolis algorithm and by applying this procedure we present a convincing analysis for the far tail regime of the order-parameter probability distribution.