Search results
Results From The WOW.Com Content Network
Schematic equal-time spin correlation functions for ferromagnetic and antiferromagnetic materials both above and below versus the distance normalized by the correlation length, . In all cases, correlations are strongest nearest to the origin, indicating that a spin has the strongest influence on its nearest neighbors.
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 ...
In the often-used z-x-z convention of Euler angles, the factor () ′ + in this formula is replaced by () ′, causing half of the functions to be purely imaginary. The realness of the d-matrix elements is one of the reasons that the z-y-z convention, used in this article, is usually preferred in quantum mechanical applications.
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics.The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1).
The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital (), where denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere.
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 ...
The argument to the function V is an element s ∈ Q Z, that is, an infinite string of spins. In the above example, the function V just picked out two spins out of the infinite string: the values s 0 and s 1. In general, the function V may depend on some or all of the spins; currently, only those that depend on a finite number are exactly solvable.
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...