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Physics Letters B

Absence of Z3 criticality in a three-dimensional Potts model with extended couplings

Frank R. Brown

Published Jul 1, 1989• 13 citations
Publisher
DOI
10.1016/0370-2693(89)91469-x

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From coupled Z3\mathbb{Z}_3Z3​ Rabi models to the Z3\mathbb{Z}_3Z3​ Potts model
We study Z3\mathbb{Z}_3Z3​-symmetric Rabi model that describes a three-level system coupled to two bosonic modes. We derive a mapping of the two-mode Z3\mathbb{Z}_3Z3​ Rabi model onto a qubit-boson ring. This mapping allows us to formulate a realistic implementation of the Z3\mathbb{Z}_3Z3​ Rabi model based on superconducting qubits. It also provides context for the previously proposed optomechanical implementation of the Z3\mathbb{Z}_3Z3​ Rabi model. In addition, we propose a physical implementation of the Z3\mathbb{Z}_3Z3​ Potts model via a coupled chain of Z3\mathbb{Z}_3Z3​ Rabi models.
We study the square-lattice three-state Potts model with the ferromagnetic next-nearest-neighbor coupling at finite temperature. Using the level-spectroscopy method, we numerically analyze the excitation spectrum of the transfer matrices and precisely determine the global phase diagram. Then we find that, contrary to a previous result based on the finite-size scaling, the massless region continues up to the decoupling point with Z3 x Z3 criticality in the antiferromagnetic region. We also check the universal relations among excitation levels to provide the reliability of our result.