Investigating the dimensional dependence of the Ising model using Monte Carlo method

Abstract

This study aims to investigate the dimensional dependence of the critical temperature of the Ising model using Monte Carlo methods. The dimensionality of the lattice is defined in accordance with the Hausdorff dimension. Our findings demonstrate a hyperbolic tangent function that relates the critical temperature with dimension. It shows a smooth step function for its behavior from 1D to 2D and 2D to 3D.