Partial equivalence of statistical ensembles and kinetic energy

Details Partial equivalence of statistical ensembles and kinetic energy Partial equivalence of statistical ensembles and kinetic energy

2007-01-15

arxiv.org/abs/cond-mat/0701339v1

Physica A 384, 318-334 (2007)

Physics

Condensed Matter

Statistical Mechanics

21 pages, 11 figures

Scientific paper

10.1016/j.physa.2007.05.043

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.

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