Showing papers on "Landau theory published in 1969"

Theory of Impurity Bands in Magnetic Fields. I. Magnetic Susceptibility

Abstract: By using the Green function method for the random lattice, the susceptibility of the impurity band in weak magnetic fields is investigated in a simplified model in which the impurity potential is attractive and of short range and the electron-electron correlation can be negligible. Simple analytical expressions for the susceptibility are obtained and are computed numerically as a function of the concentration of impurities c . When c / c 0 ( c 0 is the critical concentration at which the impurity band touches the conduction band) is very small so that the impurity band width is smaller than the binding energy of the impurity potential, the orbital susceptibility in the impurity band region is simply of the type of the atomic diamagnetism, while it is of the type of the ordinary Landau diamagnetism in the conduction band region. The result for the case c / c 0 ≫1 explains the observed discrepancy from the existing Landau theory.

Finite-Temperature Corrections to the Transport Coefficients of a Normal Fermi Liquid

Abstract: Finite-temperature corrections to the limiting low-temperature behavior of the thermal conductivity and spin-diffusion coefficient of a normal Fermi liquid are calculated using a quasiparticle Boltzmann equation which is solved by the variational method. For liquid ${\mathrm{He}}^{3}$ the most important corrections come from small momentum transfer processes, the amplitude for which can be determined exactly by using Landau theory. The expressions obtained are evaluated in detail, assuming that all Landau parameters vanish for $lg~2$, and comparison of theory with experiment yields an estimate for the previously undetermined Landau parameter ${{F}_{1}}^{a}$. The calculations are compared with calculations based on paramagnon theory.

The phase transition of the two dimensional Ising model according to a Landau theory of phase transition of second order

Abstract: The thermodynamic potential of the two dimensional Ising model is given as function of the mean value of the magnetisation which plays the role of a Landau order parameter. In this description the well known logarithmic singularity of the specific heat results from the contribution of the equilibrium fluctuations of the magnetisation in the hydrodynamic approximation.

Modified Landau Theory of the Second Order Phase Transition

Abstract: 1:he difficulty near the critical.point encountered by the Landau theory or the classical theory of the second order phase transition is removed with the least modification of the original framework. The essential point of our idea is to note that the temperature region in which the Landau theoryvalids depends sensitively on the way of defining the local order parameter. It is shown that the relations among the singularities of various thermodynamic quantities predicted by this modified form of the Landau theory are in good agreement with those obtained by nonclassical theories such as the static scaling theory. It is often pointed out that the Landau theory of the second order phase transi­ tion suffers from an internal inconsistency.1) In fact under the assumption of small ' fluctuation this theory predicts the large fluctuation at the critical point. The failure of this theory in the vicinity of the critical point, especially in the system with short range interaction, seems to be the consequence of this inconsistency. When we work with free energy density, there seems to be at least two possible ways to avoid this difficulty. One way is to take into account the higher order terms with respect to the local fluctuations and their spatial derivatives. **) The other way, which is of our main concern in this paper, is to change the defini­ tion of the local order parameter with temperature without taking into account the higher order terms. In the next section the definition of the local order parameter is carefully examIned, and this is indispensable for our whole discus­ sion. The procedure of removing the inconsistency is then presented. In § 3 the asymptotic behaviors of various thermodynamic quantities are studied and all the independent relations among the critical indices are derived which turn out to be indentical with those obtain~d by the static scaling theory.3),4) Through­ out the p:resent paper the language is used appropriate for the Ising ferromagnets though the same kind of arguments may apply to the classical gas or liquid system as well.

Spin Echoes in Terms of Spin Waves

Abstract: A general theory of linearized spin echoes in an interacting Fermi liquid is developed by expressing the results of the usual type of echo experiment directly in terms of the spin-wave normal modes of the liquid as derived from the Landau theory. The possibility of obtaining further information by observing the echoes produced by a spatially nonuniform magnetization is briefly discussed.