  In this paper we discuss the convergence rate for Galerkin approximation of
the stochastic Allen-Cahn equations driven by space-time white noise on $\T$.
First we prove that the convergence rate for stochastic 2D heat equation is of
order $\alpha-\delta$ in Besov space $\C^{-\alpha}$ for $\alpha\in(0,1)$ and
$\delta>0$ arbitrarily small. Then we obtain the convergence rate for Galerkin
approximation of the stochastic Allen-Cahn equations of order $\alpha-\delta$
in $\C^{-\alpha}$ for $\alpha\in(0,2/9)$ and $\delta>0$ arbitrarily small.
