Abstract
We show that the time-dependent Ginzburg-Landau model for a one-component order parameter coupled to a nonordering conserved density (Model C of Halperin and Hohenberg) describes the dynamic critical behavior of a certain class of ordering alloys. An equation of motion for the order parameter in scaling form is derived and used to discuss nonlinear relaxation processes that occur near the critical point after a sudden change in temperature or the symmetry-breaking field. Corresponding universal amplitude ratios are calculated to one-loop order. Unlike the dynamic critical exponent these ratios show large corrections due to fluctuations and due to the coupling to the conserved density in 4-ɛ spatial dimensions. We also verify Fisher renormalization for the model to all orders.
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Eisenriegler, E., Schaub, B. Nonlinear critical relaxation of the Ginzburg Landau field coupled to a conserved density. Z. Physik B - Condensed Matter 39, 65–74 (1980). https://doi.org/10.1007/BF01292639
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DOI: https://doi.org/10.1007/BF01292639