Self Consistent Screening Approximation For Critical Dynamics

Abstract

We generalise Bray's self-consistent screening approximation to describe the critical dynamics of the ${\varphi }^4$ 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 ansätze, 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.

21 pages, LaTeX file + 4 (EPS) figures