Mean-field theory of non-thermodynamic phase transitions for an ensemble of interacting quantum objects

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Phase transitions for an open system consisting of an ensemble of interacting quantum subsystems with discrete spectrum are studied in the mean-field approximation. In the considered model, the change of an internal symmetry of a thermodynamic system upon the second-order phase transition is due to changing symmetry of distribution of charge/spin density inside each quantum subsystem. The latter can be caused by either splitting of one of lowest degenerated energy level or closing a gap between the levels and appearance of avoided crossing. The effect of external parameters (pressure, field, composition, etc.) results in direct change of internal control parameters: level spacing and/or the strength of interaction between adjacent quantum subsystems. Considering a simplest case of the two-level quantum subsystems, expressions for the free energy as a function of the internal control parameters were obtained in analytical form. The behavior of the heat capacity and susceptibility for different regions of the low-temperature phase diagram including the area of quantum fluctuations was determined.

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E. Rozenfeld

Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences

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Email: mushnikov@imp.uran.ru
俄罗斯联邦, Ekaterinburg

N. Mushnikov

Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences

Email: mushnikov@imp.uran.ru
俄罗斯联邦, Ekaterinburg

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2. Fig. 1. Phase diagram in coordinates (ϑ, T). The arrows indicate the temperatures for which the heat capacity curves are shown in Fig. 2.

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3. Fig. 2. Dependence of heat capacity C (20) in the system of two-level quantum subsystems (10) on the level splitting ∆ = kBϑ for different temperatures.

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4. Fig. 3. Temperature dependence of heat capacity for different values ​​of ϑ/θ.

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5. Fig. 4. Contour plot of susceptibility in coordinates (ϑ, T).

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