Strange relaxation and metastable behaviors of the Ising ferromagnetic thick cubic shell

We have studied the equilibrium and nonequilibrium behaviors of the Ising ferromagnetic thick cubic shell by Monte Carlo simulation. Our goal is to find the dependence of the responses on the thickness of the shell. In the equilibrium results, we found that the pseudo-critical temperature of ferro-para phase transition of thick cubic shell increases with the increase of the thickness following a hyperbolic tangent relation. In the nonequilibrium studies, the relaxation time has been found to decrease with the increase of the thickness of the cubic shell. Here, three different regimes are found, namely rapid fall, plateau and linear region. The metastable behavior has been studied also as another kind of nonequilibrium response. The metastable lifetime has been studied as function of the thickness of the cubic shell. A nonmonotonic variation of metastable lifetime with the thickness of the shell is observed. A specified thickness for longest-lived metastability has been identified.