Phase ordering of the O(2) model in the post-gaussian approximation

Details Phase ordering of the O(2) model in the post-gaussian approximation Phase ordering of the O(2) model in the post-gaussian approximation

1996-09-17

arxiv.org/abs/cond-mat/9609163v1

Physics

Condensed Matter

43 pages, REVTeX, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.55.2300

The gaussian closure approximation previously used to study the growth kinetics of the non-conserved O(n) model is shown to be the zeroth-order approximation in a well-defined sequence of approximations composing a more elaborate theory. This paper studies the effects of including the next non-trivial correction in this sequence for the case n=2. The scaling forms for the order-parameter and order-parameter squared correlation functions are determined for the physically interesting cases of the O(2) model in two and three spatial dimensions. The post-gaussian versions of these quantities show improved agreement with simulations. Post-gaussian formulae for the defect density and the defect-defect correlation function $\tilde{g}(x)$ are derived. As in the previous gaussian theory, the addition of fluctuations allows one to eliminate the unphysical divergence in $\tilde{g}(x)$ at short scaled-distances. The non-trivial exponent $\lambda$, governing the decay of order-parameter auto-correlations, is computed in this approximation both with and without fluctuations.

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