Negative magnetic susceptibility and nonequivalent ensembles for the mean-field spin model
arXiv:cond-mat/0702004 · doi:10.1016/j.physa.2007.06.004
Abstract
We calculate the thermodynamic entropy of the mean-field spin model in the microcanonical ensemble as a function of the energy and magnetization of the model. The entropy and its derivative are obtained from the theory of large deviations, as well as from Rugh's microcanonical formalism, which is implemented by computing averages of suitable observables in microcanonical molecular dynamics simulations. Our main finding is that the entropy is a concave function of the energy for all values of the magnetization, but is nonconcave as a function of the magnetization for some values of the energy. This last property implies that the magnetic susceptibility of the model can be negative when calculated microcanonically for fixed values of the energy and magnetization. This provides a magnetization analog of negative heat capacities, which are well-known to be associated in general with the nonequivalence of the microcanonical and canonical ensembles. Here, the two ensembles that are nonequivalent are the microcanonical ensemble in which the energy and magnetization are held fixed and the canonical ensemble in which the energy and magnetization are fixed only on average by fixing the temperature and magnetic field.
14 pages, 4 figures, 2 appendices, REVTeX4
References in corpus (10)
- An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
- Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
- Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
- The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble
- Generalized canonical ensembles and ensemble equivalence
- The mean-field phi4-model: entropy, analyticity, and configuration space topology
- Application of large deviation theory to the mean-field phi^4-model
- Nonconcave entropies in multifractals and the thermodynamic formalism
- Nonconcave entropies from generalized canonical ensembles
- Comment on "First-order phase transitions: equivalence between bimodalities and the Yang-Lee theorem"