  We classify geometric blocks that serve as spin carriers into simple blocks
and compound blocks by their topologic connectivity, define their fractal
dimensions and describe the relevant transformations. By the hierarchical
property of transformations and a block-spin scaling law we obtain a relation
between the block spin and its carrier's fractal dimension. By mapping we set
up a block-spin Gaussian model and get a formula connecting the critical point
and the minimal fractal dimension of the carrier, which guarantees the
uniqueness of a fixed point corresponding to the critical point, changing the
complicated calculation of critical point into the simple one of the minimal
fractal dimension. The numerical results of critical points with high accuracy
for five conventional lattice-Ising models prove our method very effective and
may be suitable to all lattice-Ising models. The origin of fluctuations in
structure at critical temperature is discussed. Our method not only explains
the problems met in the renormalization-group theory, but also provides a
useful tool for deep investigation of the critical behaviour.
