It can be visualized as an array of rotating electrons which behave as rigid rotors that interact through short-range dipole-dipole magnetic forces originating from their magnetic dipole moments (neglecting Coulomb forces).
Although elementary quantum rotors do not exist in nature, the model can describe effective degrees of freedom for a system of sufficiently small number of closely coupled electrons in low-energy states.
[1] Suppose the n-dimensional position (orientation) vector of the model at a given site
However, it is found convenient[1] to use rotor angular momentum operators
Then, the magnetic interactions between the quantum rotors, and thus their energy states, can be described by the following Hamiltonian: where
The interaction sum is taken over nearest neighbors, as indicated by the angle brackets.
, the Hamiltonian predicts two distinct configurations (ground states), namely "magnetically" ordered rotors and disordered or "paramagnetic" rotors, respectively.
[1] The interactions between the quantum rotors can be described by another (equivalent) Hamiltonian, which treats the rotors not as magnetic moments but as local electric currents.
[2] One of the important features of the rotor model is the continuous O(N) symmetry, and hence the corresponding continuous symmetry breaking in the magnetically ordered state.
, the rotor model approximates the low-energy states of a Heisenberg antiferromagnet, with the Hamiltonian using the correspondence
[1] The particular case of quantum rotor model which has the O(2) symmetry can be used to describe a superconducting array of Josephson junctions or the behavior of bosons in optical lattices.
[3] Another specific case of O(3) symmetry is equivalent to a system of two layers (bilayer) of a quantum Heisenberg antiferromagnet; it can also describe double-layer quantum Hall ferromagnets.
[3] It can also be shown that the phase transition for the two dimensional rotor model has the same universality class as that of antiferromagnetic Heisenberg spin models.