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Spherical Model
The spherical model is a model of ferromagnetism similar to the Ising model, which was solved in 1952 by T. H. Berlin and M. Kac. It has the remarkable property that for linear dimension ''d'' greater than four, the critical exponents that govern the behaviour of the system near the critical point are independent of ''d'' and the geometry of the system. It is one of the few models of ferromagnetism that can be solved exactly in the presence of an external field. Formulation The model describes a set of particles on a lattice \mathbb containing ''N'' sites. Each site ''j'' of \mathbb contains a spin \sigma_j which interacts only with its nearest neighbours and an external field ''H''. It differs from the Ising model in that the \sigma_j are no longer restricted to \sigma_j \in \ , but can take all real values, subject to the constraint that : \sum_^N \sigma_j^2 = N which in a homogeneous system ensures that the average of the square of any spin is one, as in the usual I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone). In physics, multiple types of material magnetism have been distinguished. Ferromagnetism (along with the similar effec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-vector Model
In statistical mechanics, the ''n''-vector model or O(''n'') model is a simple system of interacting spins on a crystalline lattice. It was developed by H. Eugene Stanley as a generalization of the Ising model, XY model and Heisenberg model. In the ''n''-vector model, ''n''-component unit-length classical spins \mathbf_i are placed on the vertices of a ''d''-dimensional lattice. The Hamiltonian of the ''n''-vector model is given by: :H = K_\mathbf_i \cdot \mathbf_j where the sum runs over all pairs of neighboring spins \langle i, j \rangle and \cdot denotes the standard Euclidean inner product. Special cases of the ''n''-vector model are: :n=0: The self-avoiding walk :n=1: The Ising model :n=2: The XY model :n=3: The Heisenberg model :n=4: Toy model for the Higgs sector of the Standard Model The general mathematical formalism used to describe and solve the ''n''-vector model and certain generalizations are developed in the article on the Potts model. Reformulation as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rodney J
Rodney may refer to: People * Rodney (name) The personal name Rodney is a toponymic surname derived from the name of an unidentified place near the Somerset/ Wiltshire border. ''Rodney'' became a title of the peerage of Great Britain in 1782, as Baron Rodney. Secondarily, it came to be us ... * Rodney (wrestler), American professional wrestler Places ;Australia * Electoral district of Rodney, a former electoral district in Victoria * Rodney County, Queensland ;Canada * Rodney, Ontario, a village located within the township of West Elgin, Ontario ;New Zealand * Rodney District, a former territorial local authority district * Rodney (local board area), a local government area ** Rodney Local Board, an Auckland Council local board ** Rodney Ward, an Auckland Council ward * Rodney (New Zealand electorate), an electoral district containing most of Rodney District ;United States * Rodney, Iowa * Rodney, Mississippi, a former city * Rodney, Ohio * Rodney, Oklahoma, a ghos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curie Temperature
In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism is lost at a critical temperature. The force of magnetism is determined by the magnetic moment, a dipole moment within an atom that originates from the angular momentum and spin of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction. Permanent magnetism is caused by the alignment of magnetic moments, and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field. For example, the ordered magnetic moments (ferromagnetic, Figure 1) change and become disordered ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Zero
Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 °C on the Celsius, Celsius scale, and −459.67 °F on the Fahrenheit scale. The Kelvin and Rankine temperature scales set their zero points at absolute zero by design. This limit can be estimated by extrapolating the ideal gas law to the temperature at which the volume or pressure of a classical gas becomes zero. At absolute zero, there is no thermal motion. However, due to quantum mechanics, quantum effects, the particles still exhibit minimal motion mandated by the Uncertainty principle, Heisenberg uncertainty principle and, for a system of fermions, the Pauli exclusion principle. Even if absolute zero could be achieved, this residual quantum motion would persist. Although absolute zero can be approached, it cannot be reached. Som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Temperature
Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in mission and business critical information systems *Critical theory, a school of thought that critiques society and culture by applying knowledge from the social sciences and the humanities *Critically endangered, a risk status for wild species *Criticality (status), the condition of sustaining a nuclear chain reaction Art, entertainment, and media *Critical (novel), ''Critical'' (novel), a medical thriller written by Robin Cook *Critical (TV series), ''Critical'' (TV series), a Sky 1 TV series *Critical (Person of Interest), "Critical" (''Person of Interest''), an episode of the American television drama series ''Person of Interest'' *"Critical", a song by Abhi the Nomad from the album ''Abhi vs the Universe'', 2021 *"Critical", a 1999 sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internal Energy
The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, ''i.e.'', the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. Without a thermodynamic process, the internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics. The notion has been introduced to describe the systems characterized by temperature variations, te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. It is represented by a pseudovector M. Magnetization can be compared to Polarization density, electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics. Magnetization also describes how a material responds to an applied magnetic field as well as the way the material changes the magnetic field, and can be used to calculate the forces that result from those interactions. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the Spin (physics), spin of the electrons or the nuclei. Net magnetization results from the response of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Free Energy
In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system. The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful. The free energy is the portion of any first-law energy that is available to perform thermodynamic work at constant temperature, ''i.e.'', work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy. Several free energy functions may be formulated based on system criteria. Free energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface (mathematics)
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space. The exact definition of a surface may depend on the context. Typically, in algebraic geometry, a surface may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a topological space of dimension two; this means that a moving point on a surface may move in two directions (it has two degrees of freedom). In other words, around almost every point, there is a '' coordinate patch'' on which a two-dimensional coordinate system is defined. For example, the surface of the Earth resembles ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ising Model
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical models in physics, mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent Nuclear magnetic moment, magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a Graph (abstract data type), graph, usually a lattice (group), lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases.The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. Though it is a highly simplified model of a magnetic material, the Ising model can sti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
