Landau theory

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

Renormalization-group study of the critical end point in 4 − ε dimensions

Abstract: The phase diagrams of a variety of physical systems, among them certain antiferromagnets and ternary fluid mixtures, may include a critical line intersecting a line of first-order transitions at a critical end point rather than at the familiar tricritical point. At the critical end point the order parameter has critical fluctuations in the paramagnetic phase and a finite jump. Within Landau theory this phenomenon appears with the introduction of a negative ${\ensuremath{\varphi}}^{6}$ coupling; here we extend that theory to include fluctuations by a momentum-shell renormalization-group analysis close to four dimensions. In previous real-space analyses the critical end point was associated with a new fixed point. In contrast, the Wilson-Fisher fixed point which characterizes the entire critical line describes the critical end point here. We derive the $O(\ensuremath{\epsilon})$ corrections to the mean-field exponents which, in Landau theory, describe the approach to the critical end point from high temperatures. At the same time, the discontinuity in $〈\ensuremath{\varphi}〉$ at the critical end point predicted by Landau theory is essentially unaltered by fluctuations. It emerges from a renormalization-group calculation of the Gibbs free energy for the Ginzburg-Landau-Wilson model with a negative ${\ensuremath{\varphi}}^{6}$ term and a positive ${\ensuremath{\varphi}}^{8}$ term.

Structural phase transition in crystals with Fm3m symmetry

Abstract: A systematic study of the possible phase symmetries derived from a prototype phase with the space group Fm3m (Oh5) has been performed. These structural phase transitions involve the onset of an order parameter transforming according to one irreducible representation of the prototype space group. The investigation is performed on the basis of the Landau theory for continuous transitions. Accordingly, the irreducible representations of Fm3m are examined at the Gamma ,X,L and W high-symmetry points of the cubic face-centered Brillouin zone. The order parameters relevant to all the arms of a given star are considered. The results are summarised in several tables. These results are discussed and compared with the available experimental data relative to Fm3m subgroups.

A Landau theory of elastic incommensurate transitions

Abstract: The existence, in the free-energy expansion of a crystal, of a Lifshitz invariant related to an elastic deformation is shown to be a necessary but not sufficient condition for an elastic second-order transition leading to an incommensurate phase The necessary conditions are given and shown to be related to, but more complex than, those for the existence of acoustical activity in a crystal class