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Classical XY model information


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[1] for n = 2.

  1. ^ Stanley, H.E. (1968). "Dependence of Critical Properties on Dimensionality of Spins". Physical Review Letters. 20 (12): 589–592. Bibcode:1968PhRvL..20..589S. doi:10.1103/PhysRevLett.20.589.

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Classical XY model

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_{Y}{\begin{bmatrix}V_{XY}\\V_{YY}\end{bmatrix}}^{*}=-[X\;Y]{\begin{bmatrix}V_{XY}\\V_{YY}\end{bmatrix}}{\begin{bmatrix}V_{XY}\\V_{YY}\end{bmatrix}}^{*}...

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xy}Y_{xy}&Q_{xy}-M_{xy}+Q_{xx}Y_{xy}+Q_{xy}Y_{yy}\\Q_{yx}-M_{yx}+Q_{yx}Y_{xx}+Q_{yy}Y_{xy}&Q_{yy}-M_{yy}+Q_{yx}Y_{xy}+Q_{yy}Y_{yy}\end{bmatrix}}}...

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Jean Ginibre

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Mycin

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y}{\mathrm {d} t}}&=x(\rho -z)-y,\\[6pt]{\frac {\mathrm {d} z}{\mathrm {d} t}}&=xy-\beta z.\end{aligned}}} The equations relate the properties of a two-dimensional...

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Atomic orbital

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orbitals, and are often labeled using the associated harmonic polynomials (e.g., xy, x2 − y2) which describe their angular structure. An orbital can be occupied...

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Chaos theory

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language models as classical deterministic chaotic systems poses challenges, chaos-inspired approaches and techniques (such as ensemble modeling) may be...

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Ising, XY and Heisenberg models with 3D graphics(requires WebGL compatible browser) Ising Model code , image denoising example with Ising Model David Tong's...

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making a number of simple assumptions in order to correct the failed classical model. The assumptions included: Electrons can only be in certain, discrete...

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