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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 .
For example, for the standard ferromagnetic Potts model in , a phase transition exists for all real values , [7] with the critical point at = (+). The phase transition is continuous (second order) for 1 ≤ q ≤ 4 {\displaystyle 1\leq q\leq 4} [ 8 ] and discontinuous (first order) for q > 4 {\displaystyle q>4} .
A pair of electrons in a spin singlet state has S = 0, and a pair in the triplet state has S = 1, with m S = −1, 0, or +1. Nuclear-spin quantum numbers are conventionally written I for spin, and m I or M I for the z-axis component. The name "spin" comes from a geometrical spinning of the electron about an axis, as proposed by Uhlenbeck and ...
In atomic physics, spin–orbit coupling, also known as spin-pairing, describes a weak magnetic interaction, or coupling, of the particle spin and the orbital motion of this particle, e.g. the electron spin and its motion around an atomic nucleus. One of its effects is to separate the energy of internal states of the atom, e.g. spin-aligned and ...
Low-spin [Fe(NO 2) 6] 3− crystal field diagram. The Δ splitting of the d orbitals plays an important role in the electron spin state of a coordination complex. Three factors affect Δ: the period (row in periodic table) of the metal ion, the charge of the metal ion, and the field strength of the complex's ligands as described by the spectrochemical series.
The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative integer. Hence the allowed values of s are 0, 1 / 2 , 1, 3 / 2 , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin ...
An example of an inverse spinel is Fe 3 O 4, if the Fe 2+ (A 2+) ions are d 6 high-spin and the Fe 3+ (B 3+) ions are d 5 high-spin. In addition, intermediate cases exist where the cation distribution can be described as (A 1− x B x )[A x ⁄ 2 B 1− x ⁄ 2 ] 2 O 4 , where parentheses () and brackets [] are used to denote tetrahedral and ...
If H 2 (M,Z 2) vanishes, M is spin. For example, S n is spin for all . (Note that S 2 is also spin, but for different reasons; see below.) The complex projective plane CP 2 is not spin. More generally, all even-dimensional complex projective spaces CP 2n are not spin. All odd-dimensional complex projective spaces CP 2n+1 are spin.