  The statistical equilibrium properties of the linear sigma model are studied,
with a view towards characterizing the field configurations employed as initial
conditions for numerical simulations of the formation of disoriented chiral
condensates in high-energy nuclear collisions. The field is decomposed into its
spatial average (the order parameter) and the fluctuations (the quasi-
particles) and enclosed in a rectangular box with periodic boundary conditions.
The quantized quasi-particle modes are described approximately by Klein-Gordon
dispersion relations containing an effective mass that depends on both the
temperature and the magnitude of the order parameter. The thermal fluctuations
are instrumental in shaping the effective potential governing the order
parameter, and the evolution of its statistical distribution with temperature
is discussed, as is the behavior of the associated effective masses. As the
system is cooled the field fluctuations subside, causing a smooth change from
the high-temperature phase in which chiral symmetry is approximately restored
towards the normal phase. Of practical interest is the fact that the
equilibrium field configurations can be sampled in a simple manner, thus
providing a convenient means for specifying the initial conditions in dynamical
simulations of the non-equilibrium relaxation of the chiral field. The
corresponding correlation function is briefly considered and used to calculate
the spectral strength of radiated pions. Finally, by propagating samples of
initial configurations by the exact equation of motion, it has been ascertained
that the treatment is sufficiently accurate to be of practical utility.
