Finite-size scaling of the magnetization probability density for the critical Ising model in slab geometry

Abstract

The magnetization probability density in d=2 and 3 dimensional Ising models in slab geometry of volume $L_{\parallel}^{d-1} \times L_{\perp}$ is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio $\rho=\frac{L_{\perp}}{L_{\parallel}}$ and boundary conditions is discussed. In the limiting case $\rho \to 0$ of a macroscopically large slab ($L_{\parallel} \gg L_{\perp}$) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.