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) 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 … See more

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

• H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, (Oxford University Press, Oxford and New York 1971);
• H. Kleinert, Gauge Fields in Condensed Matter, Vol. I, " SUPERFLOW AND VORTEX LINES", … 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

• 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