Landau theory

About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.

Critical point shifts in films

Abstract: Critical behavior in thin films is discussed with attention to the example of phase separation in binary fluid mixtures between parallel plates. The analyses focus on the dependence of the shift in critical temperature ΔTc, critical field, etc., on the film thickness D, and on the nature of the walls as modeled by a surface field or chemical potential h1 which acts near the walls and leads to preferential adsorption of one of the bulk phases. Mean field theory for an Ising/lattice‐gas model is utilized and the resulting asymptotic scaling functions for the shifts ΔTc etc. are computed within Landau theory by analytic and numerical methods. Series analyses for simple cubic lattice Ising model films with h1=0 are used to estimate universal features of three‐dimensional systems: specifically, if ξ(ΔT) is the bulk correlation length, determined, say, via scattering experiments, at ΔT=T−T∞c≳0 then the shift ratio D/ξ(‖ΔTc‖) is about 2.89 for h1=0 but 4.61 for h1→∞, compared with mean field values π and 5.0699....

Elastic anomalies in minerals due to structural phase transitions

Abstract: Landau theory provides a formal basis for predicting the variations of elastic constants associated with phase transitions in minerals. These elastic constants can show substantial anomalies as a transition point is approached from both the high-symmetry side and the low-symmetry side. In the limiting case of proper ferroelastic behaviour, individual elastic constants, or some symmetry­ adapted combination of them, can become very small if not actually go to zero. When the driving order parameter for the transition is a spontaneous strain, the total excess energy for the transition is purely elastic and is given by: which has the same form as a Landau expansion. In this case, the second-order elastic constant Cik softens as a linear function of temperature with a slope in the low-symmetry phase that depends on the thermodynamic character of the transition. If the driving order parameter, Q, is some structural feature other than strain, the excess energy is given by: G = ia(T Tc )Q2 + ±bQ4 + . . . + .LAi,m,neFQn + i � Ci%eiek l,m,n l,k In this case, the effect of coupling, described by the term in AemQn, is to cause a great diversity of elastic variations depending on the values of m and n (typically 1, 2 or 3), the thermodynamic character of the transition and the magnitudes of any non-symmetry-breaking strains. The elastic constants are obtained by taking the appropriate second derivatives of G with respect to strain in a manner that includes the structural relaxation associated with Q. The symmetry properties of second-order elastic constant matrices can be related to the symmetry rules for individual phase transitions in order to predict elastic stability limits, and to derive the correct form of Landau expansion for any symmetry change. Selected examples of \"ideal\" behaviour for different types of driving order parameter, coupling behaviour and thermodynamic character have been set out in full in this review. Anomalies in the elastic properties on a macroscopic scale can also be understood in terms of the properties of acoustic phonons. These microseopie processes must be considered if elastic anomalies due to dynamical effects are to be accounted for 0935122 1/98/00 10-0693 $ 30.00 001:1 0.1127/ejm/1 0/4/0693 © 1998 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart

Exact results for interacting electrons in high Landau levels.

Abstract: We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Hamiltonian onto the {ital n}th Landau level, we show that the Hartree-Fock theory is exact in the limit {ital n}{r_arrow}{infinity}, for the high-temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature {ital T}{sub {ital t}}. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-{ital n} limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction. {copyright} {ital 1996 The American Physical Society.}

Theory of displacive phase transitions in minerals

Abstract: A lattice-dynamical treatment of displacive phase transitions leads naturally to the softmode model, in which the phase-transition mechanism involves a phonon frequency that falls to zero at the transition temperature. The basic ideas of this approach are reviewed in relation to displacive phase transitions in silicates. A simple free-energy model is used to demonstrate that Landau theory gives a good approximation to the free energy of the transition, provided that the entropy is primarily produced by the phonons rather than any configurational disorder. The "rigid unit mode" model provides a physical link between the theory and the chemical bonds in silicates and this allows us to understand the origin of the transition temperature and also validates the application of the soft-mode model. The model is also used to reappraise the nature of the structures of high-temperature phases. Several issues that remain open, such as the origin of first-order phase transitions and the thermodynamics of pressure-induced phase transitions, are discussed.