The Hamiltonian for this model can be written as the sum over i and j of the cosine of the difference between theta-sub-i and theta-sub-j, where i and j are indices of a lattice of spins.
Villain developed an approximation for this model by replacing the original Hamiltonian with a Gaussian. The correlation function in this model diverges exponentially when approaching the critical temperature from above but follows a power law when approaching from below. The change in free energy when adding a pair of singularities in this model is determined by the "helicity modulus" or "spin stiffness." Although this model does not exhibit an ordered phase, as implied by the Mermin-Wagner-Hohenberg theorem, (*) vortex excitations can drive a phase transition named for Kosterlitz and Thouless. The Hamiltonian for this model can be written as the sum over i and j of the cosine of the difference between theta-sub-i and theta-sub-j, where i and j are indices of a lattice of spins. For 10 points, identify this model of statistical mechanics which takes its name from the fact that its dimensionality is traditionally equal to 2.
Villain developed an approximation for this model by replacing the original Hamiltonian with a Gaussian.
XY model [or planar spin model]