  The two-dimensional Ising model defined on square lattices with diamond-type
bond-decorations is employed to study the nature of the ferromagnetic phase
transitions of inhomogeneous systems. The model is studied analytically under
the bond-renormalization scheme. For an $n$-level decorated lattice, the
long-range ordering occurs at the critical temperature given by the fitting
function as $(k_{B}T_{c}/J)_{n}=1.6410+(0.6281) \exp [ -(0.5857) n] $, and the
local ordering inside $n$-level decorated bonds occurs at the temperature given
by the fitting function as $(k_{B}T_{m}/J)_{n}=1.6410-(0.8063) \exp [ -(0.7144)
n] $. The critical amplitude $A_{\sin g}^{(n)}$ of the logrithmic singularity
in specific heat characterizes the width of the critical region, and it varies
with the decoration level $n$ as $A_{\sin g}^{(n)}=(0.2473) \exp [ -(0.3018) n]
$, obtained by fitting the numerical results. The cross over from a
finite-decorated system to an infinite-decorated system is not a smooth
continuation. For the case of infinite decorations, the critical specific heat
becomes a cusp with the height $c^{(n)}=0.639852$. The results are compared
with those obtained in the cell-decorated Ising model.
