  We consider the transverse field Ising model with additional all-to-all
interactions between the spins. We show that a mean-field treatment of this
model becomes exact in the thermodynamic limit, despite the presence of 1D
short-range interactions. This is established by looking for eigenstates as
coherent states with an amplitude that varies through the Hilbert space. We
study then the thermodynamics of the model and identify the different phases.
Among its peculiar features, this 1D model possesses a second-order phase
transition at finite temperature and exhibits inverse melting.
