Equivalence between microcanonical ensembles for lattice models

Abstract

The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the grand-canonical ensemble. But given that distinct ensembles are equivalent only at the thermodynamic limit, a natural question is if finite size effects would prevent such a procedure. In this work we investigate thoroughly this query in different systems yielding first- and second-order phase transitions. Our study is carried out from the direct comparison with the thermodynamic relation (∂s∂e), where the entropy s is obtained from the density of states and e is the energy per site. A systematic analysis for finite sizes is undertaken. We find that, although results become inequivalent for extremely low system sizes, the equivalence holds true for rather small L’s. Therefore direct, simple (when compared with other well established approaches) and very precise microcanonical quantities can be obtained from the proposed method.