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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.
a solid solution mixes with others to form a new solution The phase diagram in the above diagram displays an alloy of two metals which forms a solid solution at all relative concentrations of the two species. In this case, the pure phase of each element is of the same crystal structure, and the similar properties of the two elements allow for ...
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 crossover is sometimes referred to as spin transition or spin equilibrium behavior. The change in spin state usually involves interchange of low spin (LS) and high spin (HS) configuration. [2] Spin crossover is commonly observed with first row transition metal complexes with a d 4 through d 7 electron configuration in an octahedral ligand ...
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 .
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
For each angle θ between easy axis and field, equation has a solution that consists of two solution curves. It is trivial to solve for these curves by varying φ and solving for h . There is one curve for φ between 0 and π and another for φ between π and 2 π ; the solutions at φ = 0 and π correspond to h = ±∞ .
It is related to the prototypical Ising model, where at each site of a lattice, a spin {} represents a microscopic magnetic dipole to which the magnetic moment is either up or down. Except the coupling between magnetic dipole moments, there is also a multipolar version of Heisenberg model called the multipolar exchange interaction .