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  2. 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.pdf
    The 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…
     
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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

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    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

     
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