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Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
Spin network diagram, after Penrose. In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups ...
The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written m s. [ 1 ] [ 2 ] The value of m s is the component of spin angular momentum, in units of the reduced Planck constant ħ , parallel to a given direction (conventionally labelled the z –axis).
If the spin is integer then only short-range order is present. A system of half-integer spins exhibits quasi-long range order . A simplified version of Heisenberg model is the one-dimensional Ising model, where the transverse magnetic field is in the x -direction, and the interaction is only in the z -direction:
Each electron also has angular momentum in the form of quantum mechanical spin given by spin s = 1 / 2 . Its projection along a specified axis is given by the spin magnetic quantum number, m s, which can be + 1 / 2 or − 1 / 2 . These values are also called "spin up" or "spin down" respectively.
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 ...
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. [1] By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics.
A spin C structure is analogous to a spin structure on an oriented Riemannian manifold, [9] but uses the Spin C group, which is defined instead by the exact sequence 1 → Z 2 → Spin C ( n ) → SO ( n ) × U ( 1 ) → 1. {\displaystyle 1\to \mathbb {Z} _{2}\to \operatorname {Spin} ^{\mathbf {C} }(n)\to \operatorname {SO} (n ...