Spin-spin correlation function in the high-temperature Villain model

Abstract

Considers the spin-spin correlation function in the high-temperature regime of the generalised Villain model (1975). Using the 'Debye-Huckel' approximation plus systematic corrections, the authors show that this correlation function has the expected Ornstein-Zernike form (1914) and they calculate approximately the high-temperature behaviour of the correlation length. The methods presented should prove useful in matching calculations of thermodynamic quantities in the two-dimensional XY model, and in 'Debye-Huckel' analyses of a variety of two-dimensional Coulomb gas problems.