Application of the generalized Landau ansatz to second order phase transitions

The ansatz ofAmit et al. with expansion coefficients which can be nonanalytic functions of either the temperature or the order parameter is used to predict the generalized susceptibility (compressibility) and the surface tension belowT _c and the critical isotherm atT _c from the specific heat, the order parameter at the coexistence curve, and the coherence length. The results agree within 50% with experiments on different phase transitions in ferromagnets, classical gases, quantum gases, binary mixtures, and superfluid helium. The ansatz can be written in two different versions; their results differ only by logarithmic factors.     

First and second order quantum phase transitions in multi-band superconductors

In multi-band and inter-metallic materials superconductivity can be destroyed by applying external pressure in these systems. In many cases the critical temperature is driven continuously to zero, the superconducting to normal transition being associated with a superconducting quantum critical point (SQCP). In this paper we propose a model for this type of SQCP based on the increase of hybridization as pressure is applied in the material. We study a two-band superconductor with hybridization V between these bands. We use a BCS approximation and include both inter- and intra-band attractive interactions. We show that for negligible inter-band interactions, as hybridization increases there is a second order phase transition from a superconductor to a normal state at zero temperature at a critical value of the hybridization V_c. This SQCP can be reached by pressure, since this external parameter controls hybridization in the system. We also find discontinuous transitions at zero temperature and the appearance of a gapless superconducting (GS) phase in a certain range of hybridization in the case of inter-band interactions being dominant.     

Temperature dependence of EXAFS intensities near second order phase transitions

Extended x-ray absorption fine structure (EXAFS) measures near neighbor bond lengths. Thermal damping of the oscillatory absorption modulation is caused by bond-length fluctuations and is predicted to show a weak change in temperature derivative at the temperature T_c of a second order structural phase transition. The size of the slope change is a measure of the sensitivity of T_c to changes in the bond-stretching force constant.     

On the Raman activity of soft modes in the lower symmetry phase of crystals

It is shown that when a degenerate soft mode of the higher symmetry phase breaks into several modes in the lower symmetry phase, they are always Raman active in case of ferrodistortive transitions but not always Raman active in case of antiferrodistortive transitions.     

Raman active soft modes and phase transitions in sodium tungsten bronzes

The temperature dependence of the Raman spectra of Na_xWO₃ for x > 0.5 is reported. A group theoretical analysis of the data confirms the space group assignments of Clarke⁸ and supports the existence of several phases derived from rigid tilts of the WO₆ octahedra. The phase diagram for high concentration Na_xWO₃ deduced from Raman measurements is in excellent agreement with that obtained from x-ray results particularly with regard to the previously undetected tetragonal to tetragonal transition.     

Strongly first order phase transitions near an enhanced discrete symmetry point

We propose a group theoretic condition which may be applied to extensions of the Standard Model in order to locate regions of parameter space in which the electroweak phase transition is strongly first order, such that electroweak baryogenesis may be a viable mechanism for generating the baryon asymmetry of the universe. Specifically, we demonstrate that the viable corners of parameter space may be identified by their proximity to an enhanced discrete symmetry point. At this point, the global symmetry group of the theory is extended by a discrete group under which the scalar sector is non-trivially charged, and the discrete symmetry is spontaneously broken such that the discrete symmetry relates degenerate electroweak preserving and breaking vacua. This idea is used to investigate several specific models of the electroweak symmetry breaking sector. The phase transitions identified through this method suggest implications for other relics such as dark matter and gravitational waves.     

A model ferromagnet with first and second order phase transitions

A model ferromagnet with pair and four spin interaction strengths in the ratio x is shown to have classical behaviour for x > 3, and discontinuous magnetization for x ? 3, the point x = 3 corresponding to a tricritical point.     

Spectroscopy of soft modes and quantum phase transitions in coupled electron bilayers

Strongly correlated two-dimensional electrons in coupled semiconductor bilayers display remarkable broken symmetry many-body states under accessible and controllable experimental conditions. In the case of continuous quantum phase transitions (QPTs), soft collective modes drive the transformations that link distinct ground states of the electron double layers. In this paper we consider results showing that resonant inelastic light scattering methods detect soft collective modes of the double layers and probe their evolution with temperature and magnetic field. The light scattering experiments offer venues of research of fundamental interactions and continuous QPTs in low-dimensional electron liquids.     

First and second order phase transitions in gauge theories at finite temperature

We consider in general the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose lagrangian may be calculated explicitly in weak coupling perturbation theory. This lagrangian, in turn, may be investigated by means of standard ?-expansion techniques. Theories with an asymptotically free gauge coupling constant possess no stable fixed point in the ?-expansion and are inferred to have weakly first-order phase transitions; theories not satisfying this condition may have second-order transitions.     

The ferromagnetic transition of iron according to a Landau-theory of phase transitions of second order

The properties of iron at its ferromagnetic transition point are described by a type of Landau-theory developed for He II. The theory includes spatial fluctuations of the spontaneous magnetisation which lead to a logarithmic singularity of the specific heat nearT _c in agreement with measurements byKraftmakher andRomashina.     

Thermal properties of He II according to a Landau-theory of phase transitions of second order

A special type of Landau theory of second order phase transitions allows the incorporation of spatial fluctuations of the order parameter in a consistent way. The resulting theory describes the thermal properties of He II nearT _λ in agreement with experiment.     

Infrared reflectivity spectroscopy of soft modes in the vicinity of ferroelectric-paraelectric phase transitions at high temperature

The infrared reflectivity study of lithium tantalate in the ferroelectric phase up to near the transition temperature (890 K) is reported down to submillimetre wavelengths with a Fourier transform scanning infrared spectrometer.A Kramers-Krönig analysis of the reflectivity data shows the existence of a very intense soft mode, which becomes rapidly overdamped at the approach of the phase transition.The results are compared to Raman data which are controversial concerning the existence of a soft mode in this compound. Reflection spectra are fitted with a model derived from the quantum theory of the phonon self-energy.     

Calculation of the specific heat for the first order,tricritical and second order phase transitions in NH4C1

Abstract

This work presents our calculation for the specific heat C _v under an Ising model that uses our Raman frequencies of the _1/7TA (93cm ¹) and _1/5TO (144cm^?1) modes for NH₄C1. The specific heat calculation has been performed for first-order (P = 0kbar), tricritical (P=1.6kbar) and second-order (P = 2.8kbar) phase transitions in the NH₄C1 crystal. Our calculated C _v values are in good agreement with the experimentally observed Cp data from the literature for NH₄C1. This indicates that the NH₄C1 crystal can be adequately described in the lattice region by means of the Ising model studied here.     

From second to first order transitions in a disordered quantum magnet

The cross sections and transverse spin asymmetries in the hard exclusive electroproduction of decuplet baryons are calculated in the large N(c) limit and found to be comparable to that of octet baryons. Large N(c) selection rules for the production amplitudes are derived, leading to new sensitive tests of the spin aspects of the QCD chiral dynamics both in the nonstrange and strange sectors. Importance of such studies for the reliable extraction of the pion form factor from pion electroproduction is explained.     

Secondary order parameters in the structural phase transitions

In the Landau type phase transitions the primary order parameter is related with irreducible representation which subduces the high symmetry space groupG _o to the low symmetry space subgroupG andG _o G. We propose to define the secondary order parameters as irreducible representations which subduceG _o to the subgroupsH _l , whereH _l are simultaneously supergroups forG, i.e.G _o H _l G. From this statement general conclusions are drawn. In particular, for some phase transitions with elargement of the elementary cell, in addition to the superlattice reflections from the primary order parameter, the superlattice reflections from the secondary order parameters can arise in another non-equivalent high symmetry point of the reciprocal space.     

Orientational order in the vicinity of a second order smectic-A to nematic phase transition

Measurements of the quadrupolar splitting of the central N¹⁴ are reported for the liquid crystal NBOA. The splitting is a measure of the orientational order parameter. At the nematic to smectic-A transition, the orientational order parameter varies continuously as a function of temperature, but with a discontinuous slope, as expected of a second order phase transition. The results are interpreted in terms of the Kobayashi-McMillan theory.     

A general approach to specific second order ordinary differential equations using homotopy perturbation method

Homotopy perturbation method is used to solve specific second order ordinary differential equations and tested for different examples. The results obtained demonstrate efficiency of the proposed method.