  An ordered hexagonal array of aggregates can form in thin ferrofluid layers
when an external magnetic field is applied. Using the Helmholtz free energy for
this system, we calculate the optimum spacing for these aggregates. Results
show excellent agreement with experimental findings as a function of field
strength and layer thickness. Our analysis yields a crossover in the exponent
for the scaling behavior of the aggregate spacing as a function of plate
separation, in agreement with experiment. For the first time, we report a
similar crossover in the scaling behavior of the aggregate spacing as a
function of the magnetic field. The mechanisms responsible for both crossovers
are introduced and discussed.
