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 … 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 Berezinski-Kosterlitz-Thouless transition between the phases with exponentially and powerlaw decaying correlation functions. See more

• H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, (Oxford University Press, Oxford and New York 1971);
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• The existence of the thermodynamic limit for the free energy and spin correlations were proved by Ginibre, extending to this case the See more

• Classical Heisenberg model
• Coulomb gas
• Goldstone boson See more

• real-time XY model WebGL simulation
• Interactive Monte Carlo simulation of the Ising, XY and Heisenberg models with 3D graphics (requires WebGL compatible browser) See more