Equivalence between microcanonical methods for lattice models

摘要

The development of reliable methods for estimating microcanonical averagesconstitutes an important issue in statistical mechanics. One possibilityconsists of calculating a given microcanonical quantity by means of typicalrelations in the grand-canonical ensemble. But given that distinct ensemblesare equivalent only at the thermodynamic limit, a natural question is if finitesize effects would prevent such procedure. In this work we investigatethoroughly this query in different systems yielding first and second orderphase transitions. Our study is carried out from the direct comparison with thethermodynamic relation $(\frac{\partial s}{\partial e})$, where the entropy isobtained from the density of states. A systematic analysis for finite sizes isundertaken. We find that, although results become inequivalent for extreme lowsystem sizes, the equivalence holds true for rather small $L$'s. Thereforedirect, simple (when compared with other well established approaches) and veryprecise microcanonical quantities can be obtained from the proposed method.