Search results for "Landau theory"
showing 10 items of 31 documents
Phase transitions in nanosystems caused by interface motion: the Ising bipyramid with competing surface fields.
2005
The phase behavior of a large but finite Ising ferromagnet in the presence of competing surface magnetic fields +/- H_s is studied by Monte Carlo simulations and by phenomenological theory. Specifically, the geometry of a double pyramid of height 2L is considered, such that the surface field is positive on the four upper triangular surfaces of the bi-pyramid and negative on the lower ones. It is shown that the total spontaneous magnetization vanishes (for L -> infinity) at the temperature T_f(H), related to the "filling transition" of a semi-infinite pyramid, which can be well below the critical temperature of the bulk. The discontinuous vanishing of the magnetization is accompanied by a…
Theory of first-order phase transitions
1987
An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described. Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets …
Surface-directed spinodal decomposition: Lattice model versus Ginzburg-Landau theory
2009
When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglecte…
General interpolation scheme for thermal fluctuations in superconductors
2006
We present a general interpolation theory for the phenomenological effects of thermal fluctuations in superconductors. Fluctuations are described by a simple gauge invariant extension of the gaussian effective potential for the Ginzburg-Landau static model. The approach is shown to be a genuine variational method, and to be stationary for infinitesimal gauge variations around the Landau gauge. Correlation and penetration lengths are shown to depart from the mean field behaviour in a more or less wide range of temperature below the critical regime, depending on the class of material considered. The method is quite general and yields a very good interpolation of the experimental data for very…
Notes on the Electroelastic Interaction in Joint Hamiltonian and Stochastic Treatment of Polarization Response
2008
Conventional Landau theory for ferroelectric phase instability is extended by entities accounting for the violation of thermodynamic equilibrium and the impact of thermal fluctuations. The physical content concerns Ginzburg-Landau type model Hamiltonians assigned to the mean field interaction of macroscopically small and microscopically large lattice cells affected by thermal fluctuations. A special topic derived in a systematic way is long range electroelastic interaction formally given by selfconsistent solution of the polarization and strain fields. Test solution for inhomogeneous strain in a slab is presented within the framework of lattice cell picture.
Pseudo-Bosons from Landau Levels
2010
We construct examples of pseudo-bosons in two dimensions arising from the Hamiltonian for the Landau levels. We also prove a no-go result showing that non-linear combinations of bosonic creation and annihilation operators cannot give rise to pseudo-bosons.
A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields
2005
We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension 2L + 1. Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit L → ∞, the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.
Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes
2007
Nonlinear dissipative systems display the full (3+1) D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1) D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics.
Pulsating Dissipative Light Bullets
2009
Finding domains of existence for (3+1)D spatio-temporal dissipative solitons, also called “dissipative light bullets”, by direct numerical solving of a cubic-quintic Ginzburg-Landau equation (CGLE) is a lengthy procedure [1,2]. Variational approaches pave the way for quicker soliton solution mapping, as long as tractable trial functions remain suitable approximations for exact solutions [3,4].
Nematic elastomers: From a microscopic model to macroscopic elasticity theory
2008
A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-fi…