  Materials with nanoscale phase separation are considered. These materials are
formed by a mixture of several phases, so that inside one phase there exist
nanosize inclusions of other phases, with random shapes and random spatial
locations. A general approach is described for treating statistical properties
of such materials with nanoscale phase separation. Averaging over the random
phase configurations, it is possible to reduce the problem to the set of
homogeneous phase replicas, with additional equations defining the geometric
weights of different phases in the mixture. The averaging over phase
configurations is mathematically realized as the functional integration over
the manifold indicator functions. This procedure leads to the definition of an
effective renormalized Hamiltonian taking into account the existence of
competing phases. Heterophase systems with mesoscopic phase separation can
occur for different substances. The approach is illustrated by the model of a
high-temperature superconductor with non-superconducting admixture and by the
model of a ferroelectric with paraelectric random inclusions.
