Nevado Serrano, PedroPorras Torres, Diego2023-06-192023-06-192013-021951-635510.1140/epjst/e2013-01751-1https://hdl.handle.net/20.500.14352/35601© Springer Heidelberg We acknowledge QUITEMAD S2009-ESP-1594, FIS2009-10061, CAM-UCM/910758 and RyC Contract Y200200074, and COST action ”IOTA”.We present a theoretical description of a system of many spins strongly coupled to a bosonic chain. We rely on the use of a spin-wave theory describing the Gaussian fluctuations around the mean-field solution, and focus on spin-boson chains arising as a generalization of the Dicke Hamiltonian. Our model is motivated by experimental setups such as trapped ions, or atoms/qubits coupled to cavity arrays. This situation corresponds to the cooperative (E circle times beta) Jahn-Teller distortion studied in solid-state physics. However, the ability to tune the parameters of the model in quantum optical setups opens up a variety of novel intriguing situations. The main focus of this paper is to review the spin-wave theoretical description of this problem as well as to test the validity of mean-field theory. Our main result is that deviations from mean-field effects are determined by the interplay between magnetic order and mesoscopic cooperativity effects, being the latter strongly size-dependent.engjournal articlehttp://doi.org/10.1140/epjst/e2013-01751-1https://link.springer.comopen access53Phase-rransitionTrapped IonsSimulationFísica (Física)22 Física