  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.
