An explicit scheme for stochastic Allen-Cahn equations with space-time white noise near the sharp interface limit

This article investigates time-discrete approximations of Allen-Cahn type SPDEs driven by space-time white noise near the sharp interface limit $ε\to 0$, where the small parameter $ε$ is the diffuse interface thickness. We propose an explicit and easily implementable exponential integrator with a modified nonlinearity for the considered problem. Uniform-in-time and uniform-in-$ε$ moment bounds of the scheme are established and the convergence in total variation distance of order $O(T\cdot\text{Poly}(ε^{-1})τ^γ),γ