Abstract
A statistical mechanics model for two-component composites, which parallels the Ising model,
is formulated from first principles in physics. Our novel approach uses an exact representation of
the system energy, arising in the analytic continuation method of homogenization theory, which
yields a statistical mechanics framework that is both physically transparent and mathematically
tractable. The model is applied to polarized binary dielectric media in order to study liquid to
solid phase transitions occurring in electrorheological fluids.