Abstract
The one-dimensional single component Ginzburg-Landau (GL) model where the order parameter couples either linearly to an internal degree of freedom of localized defects or quadratically to rigid defects is studied. It is a model for the influence of defects on the properties of nearly ferromagnetic systems (“giant moment” formation, as proposed by Suhl) and of solids near a displacive phase transition. For isolated defects the nonlinear GL equation can be solved analytically. The exact strength and shape of the localized condensate and the conditions for its existence are calculated and used as a test for previous approximations applicable in three dimensions. Near the local “transition temperature” a localized order parameter mode becomes soft. The temperature dependence of its spectrum and shape and the phase shifts for the scattering of order parameter waves in the regions with and without localized condensate are calculated exactly. The stationary states for a system with two defects are presented. Apart from the stable states, the saddle points across which the system has to pass in going from one stable configuration to another are also discussed. The interactions between the defects induced by the order parameter field, between the localized moments corresponding to the condensate and between the defects and Bloch walls are given.
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Schmidt, H., Schwabl, F. Localized defects in a one-dimensional Ginzburg-Landau model. Z Physik B 30, 197–210 (1978). https://doi.org/10.1007/BF01320986
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DOI: https://doi.org/10.1007/BF01320986