A quantum spin model is a quantum Hamiltonian

Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...

 model that describes a system which consists of spins either interacting or not and are an active area of research in the fields of strongly correlated electron

Strongly correlated material

Strongly correlated materials are a wide class of electronic materials that show unusual electronic and magnetic properties, such as metal-insulator transitions or half-metallicity...

 systems, quantum information theory, and quantum computing. The physical observables in these quantum models are actually operators in a Hilbert space

Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...

 acting on state vectors as opposed to the physical observables in the corresponding classical spin model

Spin model

A spin model is a mathematical model used in physics primarily to explain magnetism. Spin models may either be classical or quantum mechanical in nature. Spin models have been studied in quantum field theory as examples of integrable models. Spin models are also used in quantum information theory...

s - like the ising model

Ising model

The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...

 - which are commutative variables.