Quantum clock models with infinite-range interactions

We study the phase diagram, both at zero and finite temperature, in a class of Z(q) models with infinite-range interactions. We are able to identify the transitions between a symmetry-breaking and a trivial phase by using a mean-field approach and a perturbative expansion. We perform our analysis on a Hamiltonian with 2p-body interactions and we find first-order transitions for any p > 1; in the case p = 1, the transitions are first-order for q = 3 and second-order otherwise. In the infinite-range case there is no trace of gapless incommensurate phase but, when the transverse field is maximally chiral, the model is in a symmetry-breaking phase for arbitrarily large fields. We analytically study the transition in the limit of infinite q, where the model possesses a continuous U(1) symmetry.