Universal Journal of Physics and Application Vol. 8(3), pp. 150 - 154
DOI: 10.13189/ujpa.2014.020302
Reprint (PDF) (330Kb)

Nonequivalent Ensembles for the Mean-Field φ⁶ Spin Model

S.A. Alavi ^*, S. Sarvari
Department of Physics, Hakim Sabzevari University, P. O. Box 397, Sabzevar, Iran

ABSTRACT

We derive the thermodynamic entropy of the mean field φ⁶ spin model in the framework of the micro-canonical ensemble as a function of the energy and magnetization. Using the theory of large deviations and Rugh's micro-canonical formalism we obtain the entropy and its derivatives and study the thermodynamic properties of φ⁶ spin model. The interesting point we found is that like φ⁴ model the entropy is a concave function of the energy for all values of the magnetization, but is non-concave 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 some values of the energy and magnetization in the micro-canonical formalism. This leads to the inequivalence of the micro-canonical and canonical ensembles. It is also shown that this mean-field model, displays a first-order phase transition due to the magnetic field. Finally we compare the results of the mean-field φ⁶ and φ⁴ spin models.

KEYWORDS
Statistical Mechanics, Mean-Field φ⁶ Spin Models, Ensemble Inequivalence , Non-Concave Entropies

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] S.A. Alavi , S. Sarvari , "Nonequivalent Ensembles for the Mean-Field φ⁶ Spin Model," Universal Journal of Physics and Application, Vol. 8, No. 3, pp. 150 - 154, 2014. DOI: 10.13189/ujpa.2014.020302.

(b). APA Format:
S.A. Alavi , S. Sarvari (2014). Nonequivalent Ensembles for the Mean-Field φ⁶ Spin Model. Universal Journal of Physics and Application, 8(3), 150 - 154. DOI: 10.13189/ujpa.2014.020302.