Showing papers on "Landau theory published in 1972"
TL;DR: In this article, a scaling theory for thermodynamic functions and spin correlations near the surface is developed, and relations among the exponents of the half-space are found among the sparsification terms.
Abstract: Phase transitions in Ising models with tree surfaces are studied from various points of view, including a phenomenological Landau theory, high-temperature series expansions, and a scaling theory for thermodynamic quantities and correlation functions. In the presence of a surface a number of new critical exponents must be defined. These arise because of the existence of "surface" terms in the thermodynamic functions, and because of the anisotropy of space and lack of translational symmetry introduced by the surface. The need for these new critical exponents already appears in the phenomenological theory, which is discussed in detail and related to the microscopic mean-field approximation. The essential new parameter appearing in this theory is an extrapolation length $\ensuremath{\lambda}$ which enters the boundary condition on the magnetization at the surface. For magnetic systems this length is of the order of the interaction range, in contrast to superconductors, where it is usually much larger. In order to go beyond the mean-field theory, high-temperature series expansions are carried out for the Ising half-space, to tenth order in two dimensions and to eighth order in three dimensions. A scaling theory is developed both for thermodynamic functions and for spin correlations near the surface, and relations are found among the exponents of the half-space. Both the scaling theory and the numerical calculations are compared with the exact solution of the Ising half-plane (two dimensions) by McCoy and Wu, and agreement is found wherever the theory is applicable. In analogy to the bulk situation, the scaling theory is found to agree with mean-field theory in four dimensions. The prediction of the present work which is most easily accessible to experiment is the temperature dependence of the magnetization at the surface, with critical exponent estimated to be ${\ensuremath{\beta}}_{1}=\frac{2}{3}$. The mean-field result, ${\ensuremath{\beta}}_{1}=1$, seems to agree more closely with presently available experiment, and more work is needed to clarify the situation.
320 citations
TL;DR: In this paper, X-ray scattering intensities from unoriented samples of cholesteryl nonanoate and myristate are reported for several temperatures in the smectic $A, cholesteric, and isotropic liquid phases.
Abstract: X-ray scattering intensities from unoriented samples of cholesteryl nonanoate and myristate are reported for several temperatures in the smectic $A$, cholesteric, and isotropic liquid phases. The measured Bragg-scattering intensities from the smectic planes are used to test a recent theoretical model of the smectic $A$ phase. Strong pretransition scattering (short-range-order or order-parameter fluctuations) are observed in the cholesteric phase and a Landau theory is constructed to describe this effect.
302 citations
TL;DR: In this paper, the range of validity of the Landau theory for tricritical systems is estimated by means of the Ginzburg criterion, and the conjecture that the theory also remains valid in the limiting cased=3 agrees well with measurements on He3-He4 mixtures and with numerical model calculations.
Abstract: The range of validity of the Landau theory for tricritical systems is estimated by means of the Ginzburg criterion. As a result the Landau theory seems to give an accurate description of the tricritical behaviour in some region if the dimensiond of the system is larger than 3. The conjecture that the theory also remains valid in the limiting cased=3 agrees well with measurements on He3-He4 mixtures and with numerical model calculations.
53 citations
TL;DR: In this article, the phase transition in ammonium Rochelle salt is interpreted from the group-theoretical point of view following the Landau theory of phase transition and shown to be improper since it is induced by a two-dimensional representation at k =(1/2) b 1 which correctly describes the observed phase change from the space group D 2 3 to C 2 2.
Abstract: The phase transition in ammonium Rochelle salt is interpreted from the group-theoretical point of view following the Landau theory of phase transition and shown to be improper since it is induced by a two-dimensional representation at k =(1/2) b 1 which correctly describes the observed phase change from the space group D 2 3 to C 2 2 . The expression of the free energy is given in terms of the doubly-degenerate transition parameter, besides the macroscopic polarization and deformation.
35 citations
27 citations
TL;DR: In this paper, the authors investigated the transport properties of neutron star matter in the framework of the Landau theory and found that zero sound cannot propagate in neutron star material because of very strong Landau damping.
Abstract: In the framework of the Landau theory transport properties of neutron matter are investigated. An important problem is the propagation of first and zero sound and their damping. It is found that zero sound cannot propagate in neutron star matter because of very strong Landau damping. On the other hand first sound is comparatively weakly damped. The absorption coefficient is small and depends sensitively—just as the viscosity and the relaxation time of quasi-particles—on the temperature.
12 citations
TL;DR: In this paper, the range of temperatures about the Curie temperature where the Landau theory of phase transitions fails is estimated explicitly for very weak itinerant ferromagnets, and the results are extended to finite fields and are then related to magnetic isotherms in the form of Arrott plots.
9 citations
TL;DR: In this article, anomalous properties of the thermal expansion coefficient of Invar at low temperatures are discussed on the basis of the Landau theory of a Fermi liquid, and the origin of a negative value of the coefficient at the lowest temperatures is attributed to the Landauer interaction function.
9 citations
TL;DR: In this paper, an exactly solvable model is presented that exhibits a phase transition and that can be exactly described by Landau's phase transition theory, which is used to elucidate the constructs and assumptions that go into the Landau theory, and also to illustrate the role of fluctuations near an instability in finite systems.
Abstract: An exactly solvable model is presented that exhibits a phase transition and that can be exactly described by Landau's phase transition theory. The model is used to elucidate the constructs and assumptions that go into the Landau theory, and also to illustrate the role of fluctuations near an instability in a finite system.
8 citations
TL;DR: In this paper, the behavior of superconducting, superfluid and nematic liquid-crystal films subject to various boundary conditions is investigated, and a comparative study of size effects in these several types of films leads to considerable physical insight, and their general properties at least qualitatively described by a mean-field model.
7 citations
TL;DR: For superconductors of very small size the terms in the Ginsburg-Landau free energy which describe spatial fluctuations can be neglected and the remaining terms are treated exactly and comparison with Marcelja's theory shows a slight reduction in the magnitude of the fluctuations as mentioned in this paper.
Abstract: For superconductors of very small size the terms in the Ginsburg-Landau free energy which describe spatial fluctuations can be neglected. The remaining terms are treated exactly and comparison with Marcelja's theory shows a slight reduction in the magnitude of the fluctuations. The specific heat is also calculated, and an extension to one dimensional specimens presented.
TL;DR: In this article, the spin-flop to weak ferromagnetic phase transition at 0°K was studied as a function of the parameters of the system, using a classical two sublattice model and molecular field theory.
TL;DR: In this article, the group-theoretical determination of the order parameters can be formulated in terms of the invariance properties of the Hamiltonian of the system, which avoids taking into consideration the phenomenological character of the free energy and its analytic expansion.
TL;DR: This article showed that the transition line has not necessarily a continuous slope and that it is possible to find behavior analogous to those of the tricritical points of first and second kind, analyzed by Reatto.
TL;DR: In this article, a third-moment sum rule for the spin-spin correlation function is derived and is found to have an unexpected dependence onk, i.e., one that disagrees with the corresponding Landau prediction.
Abstract: The Landau theory predicts spectral weight functions for density and spin-density fluctuations which in the long-wavelength, low-frequency limit should be equal to the true spectral weight functions of a system of interacting fermions. This correspondence plus well-known frequency sum rules provides a means to examine the Landau quasiparticle interaction parameters. Two inequalities are derived:F1 ≥G1 and another relating the first three spin-symmetric Landau coefficients to the radial distribution function and the two-particle potential. We find that the third-moment sum rule is not entirely exhausted by Landau-accountable excitations, and therefore it is the highest order sum rule which can still probe the theory. A third-moment sum rule for the spin-spin correlation function is derived and is found to have an unexpected dependence onk, i.e., one that disagrees with the corresponding Landau prediction. We do not examine this result in detail, but merely conjecture that it may indicate a basic weakness in the Landau theory of spin-density fluctuations.