Line vortices arising in the Ginzburg-Landau or Abelian Higgs model are studied numerically. For a wide range of parameters simulations of parallel line vortices and antivortices were performed and the results are reported. The head-on 90" scattering is demonstrated to be independent of initial conditions provided that the vortex zeros first completely overlap. For critically coupled vortices the scattering behavior seems to be approximately velocity independent until P-0.4 and the collisions are approximately elastic until P-0.3. This suggests that higher-order modes arising from the collisions are not excited until 6-0.3. When vortices and antivortices collide at highly relativistic speeds (P-0.9) it is found that the direction into which they reform depends upon the coupling constant. The metric on the moduli space M 2 is calculated from its field-kinetic definition. The scattering angles directly calculated from the metric components are shown to agree with the numerical simulations. The nontrivial forms of the components are discussed in relation to the scattering results.

We study the late stages of spinodal decomposition in a Ginzburg-Landau mean field model with quenched disorder. Random spatial dependence in the coupling constants is introduced to model the quenched disorder. The effect of the disorder on the scaling of the structure factor and on the domain growth is investigated in both the zero temperature limit and at finite temperature. In particular, we find that at zero temperature the domain size, R(t), scales with the amplitude, A, of the quenched disorder as R(t) = A −β f (t/A −γ ) with β ≃ 1.0 and γ ≃ 3.0 in two dimensions. We show that β/γ = α, where α is the Lifshitz-Slyosov exponent. At finite temperature, this simple scaling is not observed and we suggest that the scaling also depends on temperature and A. We discuss these results in the context of Monte Carlo and cell dynamical models for phase separation in systems with quenched disorder, and propose that in a Monte Carlo simulation the concentration of impurities, c, is related to A by A ∼ c 1/d .

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