  The paper considers heat transport in diatomic one-dimensional lattices,
containing equal amounts of particles with different masses. Ordering of the
particles in the chain is governed by single correlation parameter -- the
probability for two neighboring particles to have the same mass. As this
parameter grows from zero to unity, the structure of the chain varies from
regular staggering chain to completely random configuration, and then -- to
very long clusters of particles with equal masses. Therefore, this correlation
parameter allows a control of typical cluster size in the chain. In order to
explore different regimes of the heat transport, two interatomic potentials are
considered. The first one is an infinite potential wall, corresponding to
instantaneous elastic collisions between the neighboring particles. In
homogeneous chains such interaction leads to an anomalous heat transport. The
other one is classical Lennard-Jones interatomic potential, which leads to a
normal heat transport. The simulations demonstrate that the correlated disorder
of the particle arrangement does not change the convergence properties of the
heat conduction coefficient, but essentially modifies its value. For the
collision potential, one observes essential growth of the coefficient for fixed
chain length as the limit of large homogeneous clusters is approached. The
thermal transport in these models remains superdiffusive. In the Lennard-Jones
chain the effect of correlation appears to be not monotonous in the limit of
low temperatures. This behavior stems from the competition between formation of
long clusters mentioned above, and Anderson localization close to the
staggering ordered state.
