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- The high temperature disordered phase of the XY model is peculiar because the disordering mechanism causing this phase transition cannot be removed by any continuous transformations of the spin orientation1. In this phase, the magnetization approaches zero as the components of the spins become randomized2. Additionally, the disordered high temperature phase is characterized by an exponential decay of correlations3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.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_modeland the disordered high temperature phase is characterized by an exponential decay of correlations.ocw.mit.edu/courses/8-334-statistical-mechanics-ii …
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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 moreAs 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
• 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 … See …Wikipedia text under CC-BY-SA license Disordered XY model: Effective medium theory and beyond
Critical analysis of two-dimensional classical XY model
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Phase diagram of a square lattice model of XY Spins with …
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