Landau theory

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

Molecular dynamics study of the α–β transition in quartz: elastic properties, finite size effects, and hysteresis in the local structure

Abstract: The α–β transition in quartz is investigated by molecular dynamics simulations in the constant stress ensemble. Based on a frequently used two-body interaction potential for silica, it is found that anomalies in the elastic constants are at least in semiquantitative agreement with experiment despite the fact that no anomaly in the c/a ratio is observed in the simulations. A finite-size scaling analysis shows that first-order Landau theory is applicable to the employed model potential surface. This statement also applies to the susceptibility below the transition temperature T tr, which has not yet been measured experimentally. Examination of the local order near T tr reveals that the deformation of SiO4 tetrahedral units is equally large in the β phase as in the α phase. However, large hysteresis effects can be observed in the local structure for distances r > 4 A. The results are in agreement with the picture of a first-order displacive phase transformation which is driven by the motion of deformed tetrahedral SiO4 units. Yet, the fast oscillations of oxygen atoms are around (time-dependent) positions that do not correspond to the ideal oxygen positions in β-quartz. The averaged configurations resemble the ideal structure only if averaged over at least a few nanoseconds.

Antiferroelectric phase transition in (Sr1-xCax)TiO3 (0.12<x⩽0.40): I. Dielectric studies

Abstract: Results of a detailed dielectric study of phase transition in Sr1-xCaxTiO3 in the composition range 0.18≤x≤0.40 are reported. It is shown that the temperatures T'm and T''m corresponding to the peaks in the real (e'(T)) and imaginary (e''(T)) parts of the dielectric constant, respectively, are not only coincident but also frequency independent, suggesting that these anomalies are due to a thermodynamic phase transition and not a dipole glass/relaxor ferroelectric transition. The Curie-Weiss temperature, as determined from the e'(T) data above the transition temperature, is found to be negative. Using Landau theory considerations, the negative Curie-Weiss temperature is interpreted in terms of an antiferroelectric phase transition. It is proposed that the smearing of the e'(T) data in the composition range 0.016≤x≤0.12 reported by Bednorz and Muller is due to the frustration introduced by the antiferroelectric interactions caused by Ca2+ substitution and the ferroelectric interactions of the SrTiO3 matrix.

Landau Fermi liquid theory

Abstract: This article reviews the Landau theory of interacting Fermi liquids such as mobile electrons in solids or helium-3. It starts with Landau's original formulation which takes advantage of the existence of a Fermi surface to map the strongly interacting single-particle excitations near the Fermi surface into a system of weakly interacting quasiparticle excitations. The theory relates microscopic parameters for the quasiparticle energies and scattering strengths to experimental observables. The resulting low lying collective modes of the system, such as zero sound in helium-3, are then discussed. Next the rigorous microscopic basis of the theory is presented. Finally there is an outline of a recent modification of the theory which may resolve some of the puzzles about the nature of the electron states in materials exhibiting high transition temperature superconductivity.

Unconventional continuous phase transition in a three-dimensional dimer model.

Abstract: Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and is compatible with a tricritical universality class, at variance with previous proposals.

Derivation of the Time-Dependent Ginzburg-Landau Equation on the Line

Abstract: We give a rigorous derivation of the time-dependent one-dimensional Ginzburg—Landau equation.