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  2. The continuous version of the XY model is often used to model systems that possess order parameters with the same kinds of symmetry, e.g. superfluid helium, hexatic liquid crystals.
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    What is continuous XY model?The continuous version of the XY model is often used to model systems that possess order parameters with the same kinds of symmetry, e.g. superfluid helium, hexatic liquid crystals. This is what makes them peculiar from other phase transitions which are always accompanied with a symmetry breaking.
    What is XY model?The XY Model is another linear chain of spin-1/2 atoms but with a different type of exchange interaction in which only the x -components and y -components of the spins are involved, and with unequal weights. This system has interesting and unusual features and it is exactly soluble i.e. integrable.
    What is the XY model in two dimensions?In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices).
    Which two-dimensional XY model does not have long-range order?The two-dimensional XY model with nearest-neighbor interactions is an example of a two-dimensional system with continuous symmetry that does not have long-range order as required by the Mermin–Wagner theorem. Likewise, there is not a conventional phase transition present that would be associated with symmetry breaking.
     
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    Classical XY model - Wikipedia

    The continuous version of the XY model is often used to model systems that possess order parameters with the same kinds of symmetry, e.g. superfluid helium, hexatic liquid crystals. This is what makes them peculiar from other phase transitions which are always accompanied with a symmetry … See more

    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 … 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 … See more

    As mentioned above in one dimension the XY model does not have a phase transition, while in two dimensions it has the 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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