We introduce a quantum antiferromagnet model, having exactly soluble thermodynamic properties. It is an infinite range antiferromagnetic Ising model put in a transverse field. The free energy gives the ground state energy in the zero temperature limit and it also gives the low temperature behaviour of the specific heat, the exponential variation of which gives the precise gap magnitude in the excitation spectrum of the system. The detailed behaviour of the (random sublattice) staggard magnetisation and susceptibilities are obtained and studied near the N\'eel temperature and the zero temperature quantum critical point.