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.

10 pages, 17 images in 7 figures

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