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Partial equivalence of statistical ensembles and kinetic energy | | Lapo Casetti
; Michael Kastner
; | | Date: |
15 Jan 2007 | | Subject: | Statistical Mechanics | | Abstract: | The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a non-trivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes. | | Source: | arXiv, cond-mat/0701339 | | Services: | Forum | Review | PDF | Favorites | |
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