  Cold atom developments suggest the prospect of measuring scaling properties
and long-range fluctuations of continuous phase transitions at
zero-temperature. We discuss the conditions for characterizing the phase
separation of Bose-Einstein condensates of boson atoms in two distinct
hyperfine spin states. The mean-field description breaks down as the system
approaches the transition from the miscible side. An effective spin description
clarifies the ferromagnetic nature of the transition. We show that a difference
in the scattering lengths for the bosons in the same spin state leads to an
effective internal magnetic field. The conditions at which the internal
magnetic field vanishes (i.e., equal values of the like-boson scattering
lengths) is a special point. We show that the long range density fluctuations
are suppressed near that point while the effective spin exhibits the long-range
fluctuations that characterize critical points. The zero-temperature system
exhibits critical opalescence with respect to long wavelength waves of impurity
atoms that interact with the bosons in a spin-dependent manner.
