  The definitions of breaks and clusters in a one-dimensional chain in
equilibrium are discussed. Analytical expressions are obtained for the expected
cluster length, $\langle K \rangle$, as a function of temperature and pressure
in a one-dimensional Lennard-Jones chain. These expressions are compared with
results from molecular dynamics simulations. It is found that $\langle K
\rangle$ increases exponentially with $\beta = 1/k_BT$ and with pressure, $P$
in agreement with previous results in the literature. A method is illustrated
for using $\langle K \rangle (\beta, P)$ to generate a "phase diagram" for the
Lennard-Jones chain. Some implications for the study of heat transport in
Lennard-Jones chains are discussed.
