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

Computation of microcanonical entropy at fixed magnetization without direct counting