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Quantum clock models with infinite-range interactions. (English) Zbl 1459.82087

Summary: We study the phase diagram, both at zero and finite temperature, in a class of \({\mathbb{Z}}_q\) 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.

MSC:

82B26 Phase transitions (general) in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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