Gaussian Approach for Phase Ordering in Nonconserved Scalar Systems with Long-Range Interactions

We have applied the gaussian auxiliary field method introduced by Mazenko to the ordering dynamics of a non-conserved scalar system with attractive long-range interactions. This study provides a test-bed for the approach and shows some of the difficulties encountered in constructing a closed theory for the pair correlation function. The equation obtained for the equal-time two-point correlation function is studied in the limiting cases of small and large values of the scaling variable. A Porod regime at short distance and an asymptotic power-law decay at large distance are obtained. The theory, is not, however, consistent with the expected growth-law, and attempts to retrieve the correct growth lead to inconsistencies. These results indicate a failure of the gaussian assumption (at least in the form in which we use it) for this system.