Partial equivalence of statistical ensembles and kinetic energy
arXiv:cond-mat/0701339 · doi:10.1016/j.physa.2007.05.043
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.
21 pages, 11 figures
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Cited by in corpus (12)
- The large deviation approach to statistical mechanics
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Phase transitions and configuration space topology
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- Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
- Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
- Kinetic energy and microcanonical nonanalyticities in finite and infinite systems
- Stationary point approach to the phase transition of the classical XY chain with power-law interactions
- On a microcanonical relation between continuous and discrete spin models
- Solvable model of a self-gravitating system
- Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
- Crossover in densities of confined particles with finite range of interaction