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- 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.en.wikipedia.org/wiki/Classical_XY_model - People also ask
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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 moreThe 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 configuration, s = (sj)j ∈ Λ is an assignment of the angle −π < θj ≤ π for each j ∈ Λ.

Given a translation … See more• H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, (Oxford University Press, Oxford and New York 1971); 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 the phases with exponentially and powerlaw decaying correlation functions. See more

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