  We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature
regime, where thermal fluctuations are modeled by a random magnetic field whose
variance is proportional to the temperature. By rescaling the temperature
proportionally to the computational cell size $\Delta x$ ($T \to T\,\Delta
x/a_{\text{eff}}$, where $a_{\text{eff}}$ is the lattice constant) [M. B. Hahn,
J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures $T_{\text{C}}$
that are in line with the experimental values for cobalt, iron and nickel. For
finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie
temperature varies with the smallest size $d$ of the system. We show that the
difference between the computed finite-size $T_{\text{C}}$ and the bulk
$T_{\text{C}}$ follows a power-law of the type: $(\xi_0/d)^\lambda$, where
$\xi_0$ is the correlation length at zero temperature, and $\lambda$ is a
critical exponent. We obtain values of $\xi_0$ in the nanometer range, also in
accordance with other simulations and experiments. The computed critical
exponent is close to $\lambda=2$ for all considered materials and geometries.
This is the expected result for a mean-field approach, but slightly larger than
the values observed experimentally.
