  We study numerically the dynamical properties of the BTW model on a square
lattice for various dimensions. The aim of this investigation is to determine
the value of the upper critical dimension where the avalanche distributions are
characterized by the mean-field exponents. Our results are consistent with the
assumption that the scaling behavior of the four-dimensional BTW model is
characterized by the mean-field exponents with additional logarithmic
corrections. We benefit in our analysis from the exact solution of the directed
BTW model at the upper critical dimension which allows to derive how
logarithmic corrections affect the scaling behavior at the upper critical
dimension. Similar logarithmic corrections forms fit the numerical data for the
four-dimensional BTW model, strongly suggesting that the value of the upper
critical dimension is four.
