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Landau theory
About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.
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TL;DR: In this article, the Cauchy problem for the system where all zeros disappear after a finite time was considered. But the motion of the zeros (vortices) of u was not considered.
Abstract: We consider the Cauchy problem for the systemwhere . Let e ∈ ℝ2 with |e| = 1. If u(x, 0) is smooth, bounded andwe prove u → e uniformly in x as t → ∞. Of particular interest is the motion of the zeros (vortices) of u. In this case, all zeros disappear after a finite time.
29 citations
TL;DR: In this paper, a critical review of some theoretical results concerning the temperature dependence of the local mean square of an order parameter is given both for the region of small corrections to the results of the Landau theory and for the scaling region.
Abstract: Anomalous (non-classical) temperature behaviour of birefringence at the second-order normal-incommensurate phase transition in Rb2ZnBr4 crystals is studied experimentally. An attempt is undertaken to discuss it using the existing theoretical approach. A critical review of some theoretical results concerning the temperature dependence of the local mean square of an order parameter is given both for the region of small corrections to the results of the Landau theory and for the scaling region. It is shown that, in the region of 'small corrections' (at mod tau mod approximately=10-1), qualitative agreement of the experiment with the results of fluctuation theory can be recognised. Near the critical point, at mod tau mod <10-3, the deviation from the critical behaviour of the XY model is found; the nature of this deviation is not clear.
29 citations
TL;DR: In this article, the authors illustrate the Landau theory of phase transitions by a pedagogical example at the pre-university level, where a bead of mass is threaded on a ring which is set rotating about a vertical diameter.
Abstract: The Landau theory of phase transitions occupies a centerpiece position in physics. We illustrate the theory by a pedagogical example at the pre-university level. In the example a bead of mass is threaded on a ring which is set rotating about a vertical diameter. The dynamics of the bead mimics key features of the Landau theory.
29 citations
TL;DR: In this paper, the authors present a gauge theory for an ensemble of dislocation lines with elastic interactions as a model of melting, which is very similar to the Ginzburg-Landau theory of superconductivity.
29 citations
TL;DR: In this article, a review on the methods of the theory of singularities applied to the Landau phenomenological theory of phase transitions is presented, and a set of algorithms are presented that eliminate arbitrariness in the choice of the potential and make it possible to exclude from consideration models with nonphysical results.
Abstract: A review is presented on the methods of the theory of singularities applied to the Landau phenomenological theory of phase transitions. Constructive algorithms are presented that eliminate arbitrariness in the choice of the Landau potential and make it possible to exclude from consideration models with nonphysical results. The methods of singularity theory are illustrated by application to several real thermodynamic systems.
29 citations