Self Consistent Screening Approximation For Critical Dynamics

Details Self Consistent Screening Approximation For Critical Dynamics Self Consistent Screening Approximation For Critical Dynamics

1996-09-13

arxiv.org/abs/cond-mat/9609122v2

Physics

Condensed Matter

21 pages, LaTeX file + 4 (EPS) figures

Scientific paper

10.1088/0305-4470/30/10/013

We generalise Bray's self-consistent screening approximation to describe the critical dynamics of the $\phi^4$ theory. In order to obtain the dynamical exponent $z$, we have to make an ansatz for the form of the scaling functions, which fortunately can be much constrained by general arguments. Numerical values of $z$ for $d=3$, and $n=1,...,10$ are obtained using two different ans\"atze, and differ by a very small amount. In particular, the value of $z \simeq 2.115$ obtained for the 3-d Ising model agrees well with recent Monte-Carlo simulations.

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