Computation of Microcanonical Entropy at Fixed Magnetization Without Direct Counting

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on evaluation of saddle-point leading an optimization problem. The applied benchmark Ising model with simultaneous presence mean-field and nearest-neighbour interactions for which counting indeed possible, thus allowing comparison. Moreover, we apply mean-field, next-nearest-neighbour interactions, not straightforward. For this model, compare solution obtained by our one from formula in terms all correlation functions. This example shows that general couplings much more convenient than methods magnetization.