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that is, the set of all possible strings where k+1 spins match up exactly to a given, specific set of values ξ 0, ..., ξ k. Explicit representations for the cylinder sets can be gotten by noting that the string of values corresponds to a q -adic number , however the natural topology of the q-adic numbers is finer than the above product topology.
The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model.; In the continuum limit the Heisenberg model (2) gives the following equation of motion
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 spin 1/2 Heisenberg model in one dimension may be solved exactly using the Bethe ansatz. [1] In the algebraic formulation, these are related to particular quantum affine algebras and elliptic quantum groups in the XXZ and XYZ cases respectively. [ 2 ]
The existence of the thermodynamic limit for the free energy and spin correlations were proved by Ginibre, extending to this case the Griffiths inequality. [3]Using the Griffiths inequality in the formulation of Ginibre, Aizenman and Simon [4] proved that the two point spin correlation of the ferromagnetics XY model in dimension D, coupling J > 0 and inverse temperature β is dominated by (i.e ...
In condensed matter physics, an AKLT model, also known as an Affleck-Kennedy-Lieb-Tasaki model is an extension of the one-dimensional quantum Heisenberg spin model.The proposal and exact solution of this model by Ian Affleck, Elliott H. Lieb, Tom Kennedy and Hal Tasaki [] [1] provided crucial insight into the physics of the spin-1 Heisenberg chain.
When a manifold carries a spin C structure at all, the set of spin C structures forms an affine space. Moreover, the set of spin C structures has a free transitive action of H 2 (M, Z). Thus, spin C-structures correspond to elements of H 2 (M, Z) although not in a natural way.
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.