Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
arXiv:1005.5050 · doi:10.1088/1742-5468/2010/07/P07006
Abstract
The microcanonical entropy s(e,m) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie-Weiss-type interactions. The result shows a number of interesting properties which are peculiar to long-range interacting systems, including nonequivalence of ensembles and partial equivalence. Furthermore, from the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indistinguishable from the Curie-Weiss Ising model in canonical thermodynamics, although their microcanonical thermodynamics in general differs. The possibility of experimentally realizing quantum spin models with long-range interactions in a microcanonical setting by means of cold dipolar gases in optical lattices is discussed.
23 pages, 3 figures
References in corpus (10)
- A High Phase-Space-Density Gas of Polar Molecules
- Bose-Einstein condensation of chromium
- Statistical mechanics and dynamics of solvable models with long-range interactions
- An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
- Partial equivalence of statistical ensembles and kinetic energy
- Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
- Mean-field driven first-order phase transitions in systems with long-range interactions
- Application of large deviation theory to the mean-field phi^4-model
- Microcanonical phase diagrams of short-range ferromagnets
- Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
Cited by in corpus (10)
- Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
- Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions
- Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
- Spreading of Correlations and Entanglement in the Long-Range Transverse Ising Chain
- Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
- Ensemble inequivalence in long-range quantum systems
- Ensemble Inequivalence in Long-Range Quantum Spin Systems
- Statistical ensembles for phase coexistence states specified by noncommutative additive observables
- On the Conditions for a Quantum Violent Relaxation
- Quasi-equilibrium nonadditivity