Ising modelThe Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz 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 spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.
Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Crystallographic defectA crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect. Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization.
Electron magnetic momentIn atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment (symbol μe) is In units of the Bohr magneton (μB), it is -1.00115965218059μB, a value that was measured with a relative accuracy of 1.3e-13. The electron is a charged particle with charge −e, where e is the unit of elementary charge.
Photon polarizationPhoton polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two. The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
Nuclear Overhauser effectThe nuclear Overhauser effect (NOE) is the transfer of nuclear spin polarization from one population of spin-active nuclei (e.g. 1H, 13C, 15N etc.) to another via cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic resonance spectroscopy (NMR) is the change in the integrated intensity (positive or negative) of one NMR resonance that occurs when another is saturated by irradiation with an RF field. The change in resonance intensity of a nucleus is a consequence of the nucleus being close in space to those directly affected by the RF perturbation.
Wave vectorIn physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation. A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre.
