What makes the high temperature disordered phase of the XY model peculiar? - Search
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  2. https://en.wikipedia.org/wiki/Classical_XY_model

    • The existence of the thermodynamic limit for the free energy and spin correlations were proved by Ginibre, extending to this case the Griffiths inequality.
    • Using the Griffiths inequality in the formulation of Ginibre, Aizenman and Simon proved that the two point spin correlation of the ferromagnetics XY model in dimension D, coupling J > 0 and inverse temperature β is dominated by (i.e. has an upper bo…

    • Estimated Reading Time: 9 mins
    • People also ask
      Does the 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.
      en.wikipedia.org/wiki/Classical_XY_model
      What is the use of 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.
      en.wikipedia.org/wiki/Classical_XY_model
      What is the classical XY model in statistics?
      The classical XY model (sometimes also called classical rotor (rotator) model or O(2) model) is a lattice model of statistical mechanics.
      en.wikipedia.org/wiki/Classical_XY_model
      Does the Mermin–Wagner theorem apply to XY models?
      . 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.
      en.wikipedia.org/wiki/Classical_XY_model
    • https://pubmed.ncbi.nlm.nih.gov/21230222

      WebPhase diagram for a two-dimensional, two-temperature, diffusive XY model Phase diagram for a two-dimensional, two-temperature, diffusive XY model Phys Rev E Stat Nonlin Soft …

    • https://iopscience.iop.org/article/10.1088/0953-8984/1/30/004

      WebJul 30, 1989 · A generalisation of the two-dimensional XY model is studied using Monte Carlo simulation. In this model, two-component classical spins interact both …

      • Author: D B Carpenter, J T Chalker
      • Estimated Reading Time: 50 secs
      • Publish Year: 1989
    • https://www.researchgate.net/publication/1878653...

      WebFeb 23, 2005 · We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square …

      • Estimated Reading Time: 9 mins
      • web.mit.edu/8.334/www/grades/projects/projects12/Ahmet_Demir8_334_Project.pdf

        WebFIG. 2: The phase diagram for the modi ed XY model. The high-temperature disoirdered phase is denoted by P, the fer-romagnetic phase by F and the nematic phase by N [6]. is …

      • https://www.researchgate.net/figure/A-sketch-of...

        WebThe solid curves (red and blue), corresponding to η = 0 in eq. (2.75), separates the low temperature phase (the bounded region below it) and the high temperature phase.

      • https://web.mit.edu/8.334/www/grades/projects/projects10/YueFan.pdf

        Webfound that under low temperature, the spins are oscillating around the balanced points; under high temperature, however, the MSD linearly increases as a function of …

      • Temperature-disorder phase diagram of a three-dimensional …

        https://oa.mg/work/10.1103/physrevb.83.094203

        WebThese three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random shifts turns out to be irrelevant at …

      • XY_model - chemeurope.com

        https://www.chemeurope.com/en/encyclopedia/XY_model.html

        WebThe 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 …

      • Temperature-disorder phase diagram of a three-dimensional …

        https://link.aps.org/doi/10.1103/PhysRevB.83.094203

        WebMar 25, 2011 · These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random phase shifts turns out …

      • www.pas.rochester.edu/~stte/papers/PRB_79_214503.pdf

        Webline phase diagram within a well defined simple model. In this paper we report on one such investigation, using the three-dimensional 3D uniformly frustrated XY model with …

      • Temperature-disorder phase diagram of a three-dimensional …

        https://ui.adsabs.harvard.edu/abs/2011PhRvB..83i4203A/abstract

        WebWhile the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small σ) and a glassy phase at large disorder …

      • Anomalous elasticity in a disordered layered XY model

        https://www.semanticscholar.org/paper/Anomalous...

        WebOur data provide numerical evidence for the recently predicted anomalously elastic (sliding) intermediate phase between the conventional high-temperature and low-temperature

      • Phase diagram for a two-dimensional, two-temperature, diffusive …

        https://read.qxmd.com/read/21230222/phase-diagram...

        WebWhen the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. …

      • Correlations in the low-temperature phase of the two-dimensional …

        https://www.semanticscholar.org/paper/Correlations...

        WebAug 27, 2002 · – Monte Carlo simulations of the 2d XY model inside a square 100×100 spins (106 MCS/spin after cancellation of 106 for thermalization, cluster update algorithm). Top: …