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arXiv:cond-mat/0103566

Investigation of thermodynamic properties of pseudospin-electron model in the gaussian fluctuation approximation

Kyrylo V Tabunshchyk

Published Mar 27, 2001• 0 citations
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Abstract

A method of consideration of gaussian fluctuations of the effective mean field within the framework of the GRPA scheme is applied to investigation of thermodynamical properties of a pseudospin-electron model (PEM). The grand canonical potential, pseudospin mean value, as well as the mean squares of fluctuations are calculated. Obtained results are compared with corresponding ones obtained by other approximations. An influence of the gaussian fluctuations of mean field on the thermodynamic properties of PEM is discussed.

DOI
10.48550/arxiv.cond-mat/0103566

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A method of consideration of gaussian fluctuations of the effective mean field within the framework of the GRPA scheme is applied to investigation of thermodynamical properties of a pseudospin-electron model (PEM). The grand canonical potential, pseudospin mean value, as well as the mean squares of fluctuations are calculated. Obtained results are compared with corresponding ones obtained by other approximations. An influence of the gaussian fluctuations of mean field on the thermodynamic properties of PEM is discussed.
Energy spectrum and thermodynamics of the pseudospin{electron model are investigated in the dynamical mean eld approximation (d = 1 limit).In the limit of zero electron correlation this model is analytically exactly soluble within this approach: in the = const regime the rst order phase transition with the jump of the pseudospin mean value and reconstruction of the electron spectrum can be realized, while in the n = const regime the phase separation in electron subsystem can take place for certain values of the model parameters.On the basis of the obtained results the applicability of the approximate schemes previously used for the investigation of the pseudospin{ electron model are discussed.
In order to contribute to understand well the finite-temperature properties of the Falicov-Kimball model, we study the temperature dependence of the specific heat, internal energy, entropy, and mean square fluctuation of the difference between the ion and electron numbers, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model. For this purpose we used the method of small-cluster exact-diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined Falicov-Kimball model exhibits behavior of alternate electron-ion short-range ordering at low temperature, and gradual metal-insulator transition at high temperature, but, does not exhibit the crossing point of the specific heat curves, characteristic of the Hubbard model.
Abstract Using the semi-classical (Thomas–Fermi) approximation, the thermodynamic properties of ideal Fermi gases in a harmonic potential in an n -dimensional space are studied under the generalized uncertainty principle (GUP). The mean particle number, internal energy, heat capacity and other thermodynamic variables of the Fermi system are calculated analytically. Then, analytical expressions of the mean particle number, internal energy, heat capacity, chemical potential, Fermi energy, ground state energy and amendments of the GUP are obtained at low temperatures. The influence of both the GUP and the harmonic potential on the thermodynamic properties of a copper-electron gas and other systems with higher electron densities are studied numerically at low temperatures. We find: (1) When the GUP is considered, the influence of the harmonic potential is very much larger, and the amendments produced by the GUP increase by eight to nine orders of magnitude compared to when no external potential is applied to the electron gas. (2) The larger the particle density, or the smaller the particle masses, the bigger the influence of the GUP. (3) The effect of the GUP increases with the increase in the spatial dimensions. (4) The amendments of the chemical potential, Fermi energy and ground state energy increase with an increase in temperature, while the heat capacity decreases. T F0 is the Fermi temperature of the ideal Fermi system in a harmonic potential. When the temperature is lower than a certain value (0.22 times T F0 for the copper-electron gas, and this value decreases with increasing electron density), the amendment to the internal energy is positive, however, the amendment decreases with increasing temperature. When the temperature increases to the value, the amendment is zero, and when the temperature is higher than the value, the amendment to the internal energy is negative and the absolute value of the amendment increases with increasing temperature. (5) When electron density is greater than or equal to 10 37 m −3 , the influence of the GUP becomes the dominant factor affecting the thermodynamic properties of the system.
Exact results for the thermodynamic properties and mean occupation numbers of a system of noninteracting fermions with equidistant level spacing are presented for an arbitrary number of particles. It is discussed quantitatively how the results converge to the corresponding ones in the grand canonical ensemble when the thermodynamic limit is reached. From the simple calculations it also follows that the thermodynamics of an infinite two-dimensional electron gas is identical to that of a one-dimensional harmonic chain with linearized dispersion. The results generalize and simplify previous approaches to this model published in this journal.
This paper investigates the role of statistical fluctuations about the equilibrium value of the order parameter in the vicinity of a phase-transition temperature. The systems under consideration are assumed to be of finite size, but the behavior in the thermodynamic limit is also described. Our objective is to examine the simplest exactly solvable model of non-Gaussian static fluctuations for samples of finite size. To this end a Landau form is employed for the model Hamiltonian and various expansions are analyzed in order to describe first- and second-order phase transitions, field-induced transitions, and liquid-vapor critical phenomena. The approach differs from previous treatments primarily in the application of a quartic non-Gaussian model for statistical fluctuations which redresses some of the shortcomings of the standard Gaussian approximation. In particular, it is found that for finite values of V (volume) no singularities exist even at the critical temperature. The treatment is generalized by examining a class of non-Gaussian distribution functions, and particular emphasis is placed on strict adherence to the uniform convergence criterion so that general conclusions can be drawn.