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

TL;DR

This study investigates how the probability density of magnetization in 2D and 3D critical Ising models scales with system size and shape in slab geometries, revealing Gaussian behavior in large slabs.

Contribution

It provides the first detailed finite-size scaling analysis of magnetization distribution in slab geometries at criticality for Ising models.

Findings

Distribution scales as Gaussian in large slabs

Finite-size scaling depends on aspect ratio and boundary conditions

Results confirmed through Monte Carlo simulations

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.