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- The XY model for spin is a statistical mechanical model that describes the behavior of spins on a lattice123. In this model:
- Each spin can take on any angle between 0 and 2π.
- The energy is given by E = − J∑ < ij > cos(θi − θj), where J is the interaction energy1.
- The quantum XY spin chain is a one-dimensional version of this model3.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.The XY model (sometimes called the planar model) consists of spins on a lattice where each spin can take on any angle θi between 0 and 2π. The energy is given by E = − J∑ < ij > cos(θi − θj), where J is the interaction energy that sets the scale for the energy.www.compadre.org/stpbook/statistical-mechanics-…The Classical XY-Model is a statistical mechanical model of spin interactions which may be used to predict magnetic behaviour. For a two dimensional lattice of ~ G side length N, the spin may be given as a complex number of unit length where ~x = exp(i ~x) = cos(~x) + i sin(~x)www.maths.tcd.ie/~robinson/labs/monte.pdfThe quantum XY spin chain is a one-dimensional statistical mechanics model used to understand the behavior of materials through their microscopic quantum spins and their interactions with their nearest neighbors.csc.ucdavis.edu/~chaos/courses/poci/Projects2017… - People also ask
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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 n = 2. See more
Given a D-dimensional lattice Λ, per each lattice site j ∈ Λ there is a two-dimensional, unit-length vector sj = (cos θj, sin θj)
The spin configuration, s = (sj)j ∈ Λ is an assignment of the … See more• The existence of the thermodynamic limit for the free energy and spin correlations were proved by Ginibre, extending to this case the See more
As mentioned above in one dimension the XY model does not have a phase transition, while in two dimensions it has the Berezinski-Kosterlitz-Thouless transition between … See more
• H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, (Oxford University Press, Oxford and New York 1971); See more
Wikipedia text under CC-BY-SA license Realizing the classical XY Hamiltonian in polariton simulators
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