What will be the Euclidean dimension of an Ising ferromagnetic cubic shell?

Abstract

The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic shell have been extensively studied by Monte Carlo simulation using Metropolis single spin flip algorithm. Although geometrically the Euclidean dimension of the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell undergoes ferromagnetic phase transition at a temperature which is very close to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising ferromagnetic cubic shell shows a strange (neither exponential nor stretched exponential) kind of relaxation behaviour, instead of exponential relaxation as usually observed in the two dimensional Ising ferromagnet. The metastable lifetime of a ferromagnetic Ising cubical shell is studied as a function of the applied magnetic field. Here also, the cubic shell behaves more likely a two-dimensional object as found from statistical analysis and comparison with Becker-D\"oring prediction of classical nucleation theory.