Abstract
The Kittel–Shore Hamiltonian characterizes N spins with identical long-range interactions, and the 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, 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. Additionally, we extend the framework to complex deformations on the unit circle, q = e
iθ
, for q not being a root of unity. For an N = 4 tetrahedral cluster, this phase establishes a thermodynamic equivalence between a second-neighbor spin-Hamiltonian and the q-deformed quantum model. At least, we have found experimental compounds well reproduced by the Kittel–Shore model for N = 4. Validating our effective algebraic model against exact diagonalisation data for the Cu
2
Te
2
O
5
X
2
(X = Cl, Br) compound family demonstrates that θ accurately reproduces the structural anisotropy.