Thermodynamic Bethe ansatz for the AII sigma-models

We derive thermodynamic Bethe ansatz equations describing the vacuum energy of the SU(2N)/Sp(N) nonlinear sigma model on a cylinder geometry. The starting points are the recently-proposed amplitudes for the scattering among the physical, massive excitations of the theory. The analysis fully confirms the correctness of the S-matrix. We also derive closed sets of functional relations for the pseudoenergies (Y-systems). These relations are shown to be the k-->infinity limit of the Sp(k+1)-related systems studied some years ago by Kuniba and Nakanishi in the framework of lattice models.