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XY Model
The classical XY model (sometimes also called classical rotor (rotator) model or O(2) model) is a lattice model of statistical mechanics. In general, the XY model can be seen as a specialization of Stanley's ''n''-vector model for . Definition Given a -dimensional lattice , per each lattice site there is a two-dimensional, unit-length vector The ''spin configuration'', is an assignment of the angle for each . Given a ''translation-invariant'' interaction and a point dependent external field \mathbf_=(h_j,0), the ''configuration energy'' is : H(\mathbf) = - \sum_ J_\; \mathbf_i\cdot\mathbf_j -\sum_j \mathbf_j\cdot \mathbf_j =- \sum_ J_\; \cos(\theta_i-\theta_j) -\sum_j h_j\cos\theta_j The case in which except for nearest neighbor is called ''nearest neighbor'' case. The ''configuration probability'' is given by the Boltzmann distribution with inverse temperature : :P(\mathbf)=\frac \qquad Z=\int_ \prod_ d\theta_j\;e^. where is the normalization, or partition fun ...
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Jean Ginibre
Jean Ginibre (4 March 1938 — 26 March 2020) was a French mathematical physicist. He is known for his contributions to random matrix theory (see circular law), statistical mechanics (see FKG inequality, Ginibre inequality), and partial differential equations. With Martine Le Berre and Yves Pomeau, he provided a kinetic theory for the emission of photons by an atom maintained in an excited state by an intense field that creates Rabi oscillations. He received the Paul Langevin Prize in 1969. Jean Ginibre was Emeritus Professor at Paris-Sud 11 University. He directed the thesis of Monique Combescure. See also *Classical XY model The classical XY model (sometimes also called classical rotor (rotator) model or O(2) model) is a lattice model of statistical mechanics. In general, the XY model can be seen as a specialization of Stanley's ''n''-vector model for . Definition ... References 1938 births 2020 deaths French mathematicians French physicists French mathema ...
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Lattice Model (physics)
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model. The exact solution to many of these models (when they are solvable) includes the presence of solitons. Techniques for solving these include the inverse scattering transform and the method of Lax pairs, the Yang–Baxter equation and quantum groups. The solution of these models has ...
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Helmholtz Free Energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature ( isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium. In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant ''pressure''. For example, in explosives research Helmholtz free energy is often used, since explosive reactions by their nature induce pressure changes. It is also frequently used to define fundamental equations of state of pure substances. The concept of free energy was developed by Hermann von Helmholtz, ...
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Potts Model
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics. The strength of the Potts model is not so much that it models these physical systems well; it is rather that the one-dimensional case is exactly solvable, and that it has a rich mathematical formulation that has been studied extensively. The model is named after Renfrey Potts, who described the model near the end of his 1951 Ph.D. thesis. The model was related to the "planar Potts" or " clock model", which was suggested to him by his advisor, Cyril Domb. The four-state Potts model is sometimes known as the Ashkin–Teller model, after Julius Ashkin and Edward Teller, who considered an equivalent model in 1943. The Potts model is related to, and generalized by, several other models, including the XY model, ...
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Metropolis Algorithm
A metropolis () is a large city or conurbation which is a significant economic, political, and cultural area for a country or region, and an important hub for regional or international connections, commerce, and communications. A big city belonging to a larger urban agglomeration, but which is not the core of that agglomeration, is not generally considered a metropolis but a part of it. The plural of the word is ''metropolises'', although the Latin plural is , from the Greek (). For urban areas outside metropolitan areas that generate a similar attraction on a smaller scale for their region, the concept of the regiopolis ("regio" for short) was introduced by urban and regional planning researchers in Germany in 2006. Etymology () is a Greek word, (plural: ) coming from , meaning "mother" and , meaning "city" or "town", which is how the Greek colonies of antiquity referred to their original cities, with whom they retained cultic and political-cultural connections. The wo ...
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Monte Carlo
Monte Carlo ( ; ; or colloquially ; , ; ) is an official administrative area of Monaco, specifically the Ward (country subdivision), ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to a larger district, the Monte Carlo Quarter (corresponding to the former municipality of Monte Carlo), which besides Monte Carlo/Spélugues also includes the wards of Saint Roman, Monaco, La Rousse/Saint Roman, Larvotto, Larvotto/Bas Moulins and Saint Michel, Monaco, Saint Michel. The permanent population of the ward of Monte Carlo is about 3,500, while that of the quarter is about 15,000. Monaco has four traditional quarters, from west to east they are: Fontvieille, Monaco, Fontvieille (the newest), Monaco City, Monaco-Ville (the oldest), La Condamine, and Monte Carlo. Monte Carlo is situated on a prominent escarpment at the base of the Maritime Alps along the French Riviera. Near the quarter's western end is the "world-famous Place du Ca ...
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Symmetry Breaking
In physics, symmetry breaking is a phenomenon where a disordered but Symmetry in quantum mechanics, symmetric state collapses into an ordered, but less symmetric state. This collapse is often one of many possible Bifurcation theory, bifurcations that a particle can take as it approaches a lower energy state. Due to the many possibilities, an observer may assume the result of the collapse to be arbitrary. This phenomenon is fundamental to quantum field theory (QFT), and further, contemporary understandings of physics. Specifically, it plays a central role in the Glashow–Weinberg–Salam model which forms part of the Standard model modelling the electroweak sector.In an infinite system (Minkowski space, Minkowski spacetime) symmetry breaking occurs, however in a finite system (that is, any real super-condensed system), the system is less predictable, but in many cases Quantum tunnelling, quantum tunneling occurs. Symmetry breaking and tunneling relate through the collapse of a p ...
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Phase Transition
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of matter, states of matter: solid, liquid, and gas, and in rare cases, plasma (physics), plasma. A phase of a thermodynamic system and the states of matter have uniform physical property, physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition States of matter Phase transitions commonly refer to when a substance tran ...
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Mermin–Wagner Theorem
In quantum field theory and statistical mechanics, the Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions . Intuitively, this theorem implies that long-range fluctuations can be created with little energy cost, and since they increase the entropy, they are favored. This preference is because if such a spontaneous symmetry breaking occurred, then the corresponding Goldstone bosons, being massless, would have an infrared divergent correlation function. The absence of spontaneous symmetry breaking in dimensional infinite systems was rigorously proved by David Mermin and Herbert Wagner (physicist), Herbert Wagner (1966), citing a more general unpublished proof by Pierre Hohenberg (published later in 1967) in statistical mechanics. ...
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XY Magnetisation
XY, or xy, or any of its variants may refer to: Entertainment * '' Pokémon X'' and ''Y'', a pair of 2013 role-playing video games in the ''Pokémon'' series * ''XY'' (magazine), a gay male youth magazine that also operated a personals website * ''X, Y'', a 1993 novel by Michael Blumlein * '' X&Y'', a 2005 album by Coldplay * Xy, a member of the band Samael Film and television * '' Aktenzeichen XY… ungelöst'', a German television series first broadcast in 1967 * ''Kyle XY'', an American sci-fi television series first broadcast in 2006 * '' Pokémon the Series: XY'', the 17th season of ''Pokémon'' and the first and titular season of ''Pokémon the Series: XY'', first broadcast in 2013; named after the games * ''X+Y'', a 2014 British film * '' X/Y'', a 2014 American film * ''X&Y'' (film), a 2018 Swedish film * "XY", an episode of the 8th season of the television series ''Castle'', first broadcast in 2018 * ''XY Chelsea'', a 2019 American-British documentary film about C ...
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Curie Constant
Curie may refer to: *Curie family, a family of distinguished scientists: :* Jacques Curie (1856–1941), French physicist, Pierre's brother :* Pierre Curie (1859–1906), French physicist and Nobel Prize winner, Marie's husband :* Marie Skłodowska–Curie (1867–1934), Polish chemist and physicist, two-time Nobel Prize winner, Pierre's wife :* Irène Joliot-Curie (1897–1956), French physicist and Nobel Prize winner, Pierre and Marie's daughter :* Frédéric Joliot-Curie (1900–1958), French physicist and Nobel Prize winner, Irène's husband :*Ève Curie (1904–2007), French-American journalist and pianist, Pierre and Marie's daughter :* Henry Richardson Labouisse (1904–1987), American diplomat and director of UNICEF, Ève's husband Things and ideas named after the Curie family Scientific concepts, inventions and discoveries * Curie (unit) (Ci), unit of radioactivity * Curie (lunar crater) * Curie (Martian crater) * Curie (rocket engine), a liquid-propellant engine ...
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