  We present the exact thermodynamics (isochores, isotherms, isobars, response
functions) of a statistically interacting quantum gas in D dimensions. The
results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear
Schroedinger model, a gas with repulsive two-body contact potential. In all
dimensions the ideal boson and fermion gases are recovered in the weak-coupling
and strong-coupling limits, respectively. For all nonzero couplings ideal
fermion gas behavior emerges for D>>1 and, in the limit D->infinity, a phase
transition occurs at T>0. Significant deviations from ideal quantum gas
behavior are found for intermediate coupling and finite D.
