Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-12-29
Physics
Condensed Matter
Statistical Mechanics
10 pages, 4 figures
Scientific paper
We derive the thermodynamic entropy of the maen-field $\phi^{6}$ spin model in the framework of microcanonical ensemble as a function of the energy and magnetization. Using the theory of large deviations and Rugh's microcanonical formalism we obtain the entropy and its derivatives and study the thermodynamic properties of $\phi^{6}$ spin model. The interesting point we found is that like $\phi^{4}$ model 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 means that the magnetic susceptibility of the model can be negative for fixed values of the energy and magnetization in the microcanonical formalism. This leads to the inequivalence of the microcanonical and canonical ensembles. It is also shown that this mean-field model,displays a first-order phase transition driven by the magnetic field. Finally we compare the results of the mean-field $\phi^{6}$ and $\phi^{4}$ spin models.
Alavi S. A.
Sarvari S.
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