  We study the thermodynamics of short-range interacting, two-dimensional
bosons constrained to the lowest Landau level. When the temperature is higher
than other energy scales of the problem, the partition function reduces to a
multidimensional complex integral that can be handled by classical Monte Carlo
techniques. This approach takes the quantization of the lowest Landau level
orbits fully into account. We observe that the partition function can be
expressed in terms of a function of a single combination of thermodynamic
variables, which allows us to derive exact thermodynamic relations. We
determine the asymptotic behavior of this function and compute some
thermodynamic observables numerically.
