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We prove refined space-time regularity for the classical stochasticAllen-Cahn equation with logarithmic potential. This allows to establish arandom separation property, i.e. that the trajectories of the solution arestrictly separated from the potential barriers. The present contributionextends the results obtained in Bertacco et al. (2022), where separation wasproved only for $p$-Laplace operators with $p$ greater than thespace-dimension.

A note on regularity and separation for the stochastic Allen-Cahn equation with logarithmic potential