Thermodynamics of the $q$-deformed Kittel--Shore model

The Kittel–Shore Hamiltonian characterizes $N$ spins with identical long-range interactions, and the $\mathfrak{su}(2)$ coalgebra has been proven to be a symmetry of this model, which can be exactly solved. By using quantum groups and, in particular, $\mathfrak{su}_{q}(2)$, this Hamiltonian was deformed. In this work, we study the thermodynamic properties of this deformed model for spin-$1/2$ particles. In particular, we discuss how this deformation affects the specific heat, magnetic susceptibility, magnetisation, and phase transitions as a function of the parameter $q$ of the deformation and compare them with those of the undeformed model. Deformation was found to shift the thermodynamic behaviours to higher temperatures and alter the phase transitions. The potential applications of this $q$-deformed model for describing few-spin quantum systems with non-identical couplings are discussed.

💡 Research Summary

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The paper investigates the thermodynamic behavior of a q‑deformed version of the Kittel‑Shore (KS) model for spin‑½ particles. The original KS Hamiltonian describes N spins interacting with identical long‑range coupling I on a complete graph and possesses an su(2) coalgebra symmetry that allows an exact solution in terms of total angular momentum J and its z‑component m. By replacing the underlying symmetry algebra with the quantum group Uq(su(2)), the authors construct a deformed Hamiltonian that reduces to the original one when the deformation parameter q equals 1 (η = 0). For spin‑½ the ladder operators J± remain q‑independent, but the Casimir operator and the energy eigenvalues acquire q‑integer factors:

E_q(N,J,m) = –(I/2)(