Thermodynamics of a statistically interacting quantum gas in D dimensions

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 Schrodinger 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.