  The possibility of materials that are governed by a fixed point related to
small world networks is discussed. In particular, large-scale Monte Carlo
simulations are performed on Ising ferromagnetic models on two different
small-world networks generated from a one-dimensional spin chain. One has the
small-world bond strengths independent of the length, and exhibits a
finite-temperature phase transition. The other has small-world bonds built from
atoms, and although there is no finite-temperature phase transition the system
shows a slow power-law change of the effective critical temperature of a finite
system as a function of the system size. An outline of a possible synthesis
route for quasi small-world nanomaterials is presented.
