Landau theory

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

Landau theory of the crumpling transition.

Abstract: An order-parameter theory of the crumpling transition in $D$-dimensional polymerized membranes embedded in $d$ dimensions is developed. Within mean-field theory, we show how self-avoidance modifies the behavior at the second-order crumpling transition. Fluctuations drive the transition first order to lowest order in $\ensuremath{\epsilon}=4\ensuremath{-}D$, for $dl{d}_{c}\ensuremath{\approx}219$.

Coexistence curve of polystyrene in methylcyclohexane. I. Range of simple scaling and critical exponents

Abstract: We have measured coexistence curves for the system polystyrene–methylcyclohexane with varying molecular weight from Mw=1.02×104 to 71.9×104. In the temperature range e=(Tc−T)/Tc≳0.03, a deviation from simple scaling was observed for systems with Mw=10.9∼71.9×104. The effect of correction terms on simple scaling was negligibly small for systems with Mw=1.02∼4.64×104. This finding is compatible with molecular weight dependence of a critical value of e for the validity of the Landau theory. In the appropriate temperature range, where a contribution from the correction terms is negligible, an analysis by simple scaling gives the exponent β=0.332±0.001 independent of molecular weight. The critical exponent for the diameter is also independent of molecular weight and determined as 0.858±0.005, which is consistent with results of recent specific heat measurements.

Shape phase transitions and critical-point phenomena in atomic nuclei

Abstract: Atomic nuclei exhibit phase transitions as a function of the number of their constituent protons and neutrons. These phase transitions are not of the usual thermodynamic type, but rather they are quantum phase transitions in the equilibrium shape and structure of the ground and low-lying states. This realization has sparked a new area of research, focusing on the concept of 'critical-point symmetries', which describe the structure of nuclei at phase-transitional points. Both macroscopic (geometric or algebraic) and microscopic (shell-model) aspects of these phase transitions and of changes in structure with proton and neutron number in nuclei are discussed, along with an interpretation in terms of simple Landau theory. Finally, some alternative scenarios and schematic models for different classes of nuclei based on other simple potentials are briefly summarized.

Landau levels in the presence of topological defects

Abstract: In this paper we study the Landau levels in the presence of topological defects. We analyse the behaviour of electrons moving in a magnetic field in the presence of a continuous distribution of disclinations, a magnetic screw dislocation and a dispiration. We focus on the influence of these topological defects on the spectrum of the electron (or hole) in the magnetic field in the framework of the geometric Katanaev-Volovich theory of defects in solids. The presence of the defect breaks the degeneracy of the Landau levels in different ways depending on the defect. Exact expressions for energies and eigenfunctions are found for all cases. Using Kaluza-Klein theory we solve the Landau level problem for a dispiration and compare the results with the ones obtained in the previous cases.