What makes the high temperature disordered phase of the XY model peculiar? - Search
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  2. The peculiar nature of the disordering mechanism causing this phase transition, is that these disorders cannot be removed by any continuous transformations of the spin orientation.
    web.mit.edu/8.334/www/grades/projects/projects12…
    Rigorous analysis of the XY model shows the magnetization in the thermodynamic limit is zero, and that the square magnetization approximately follows, which vanishes in the thermodynamic limit. Indeed, at high temperatures this quantity approaches zero since the components of the spins will tend to be randomized and thus sum to zero.
    en.wikipedia.org/wiki/Classical_XY_model
    and the disordered high temperature phase is characterized by an exponential decay of correlations.
    ocw.mit.edu/courses/8-334-statistical-mechanics-ii …
     
  3. People also ask
    What is a high-temperature disordered phase with exponential correlation decay?It is a phase transition of infinite order. In the 2-D XY model, vortices are topologically stable configurations. It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices.
    Does XY model have a ferromagnet-paramagnet phase transition?In three and higher dimensions the XY model has a ferromagnet-paramagnet phase transition. At low temperatures the spontaneous magnetization is nonzero: this is the ferromagnetic phase. As the temperature is increased, spontaneous magnetization gradually decreases and vanishes at a critical temperature.
    Does XY model have phase transitions at finite temperature?Indeed, like the one-dimensional Ising model, the one-dimensional XY model has no phase transitions at finite temperature. The same computation for periodic boundary condition (and still h = 0) requires the transfer matrix formalism, though the result is the same. (Click "show" at right to see the details of the transfer matrix formalism.)
    What is the difference between XY model and ferromagnetic model?The XY model at zero temperature in the absence of an external field has all spins aligned in a particular direction corresponding to a ferromagnetic phase and shows long-range order while at high temperatures it is in a symmetric paramagnetic phase in which all the directions on the plane are equivalent for all spins.
     
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    Classical XY model - Wikipedia

    Topological defects in the XY model lead to a vortex-unbinding transition from the low-temperature phase to the high-temperature disordered phase. Indeed, the fact that at high temperature correlations decay exponentially fast, while at low temperatures decay with power law, even though in both regimes … 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

    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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