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 and computability theory in theoretical computer science. The theory of spin models is far reaching and unifying topic that cuts across many fields.

Introduction

In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar.

The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions.

See also

• Ising model
• Classical Heisenberg model
• Quantum Heisenberg model
• Quantum rotor model
• Kuramoto model
• ANNNI model
• Potts model
• XY model
• Hubbard model
• t-J model
• J1 J2 model
• Bethe ansatz
• Yang–Baxter equation
• Magnetism
• Spin
• Spin waves
• Spin stiffness
• Majumdar–Ghosh model

References

• Zur Theorie der Metalle doi:10.1007/BF01341708
• R.J. Baxter, Exactly solved models in statistical mechanics, London, Academic Press, 1982
• Ian Affleck, "Large-n limit of the Heisenberg–Hubbard model: Implications for high-Tc superconductor", Phys. Rev. B 37, 3774–3777 (1988) doi:10.1103/PhysRevB.37.3774

External links

• Introduction to classical and Ising Spin Models
• Quantum Field Theory of Many-Body Systems
• Institute of Quantum Information Caltech