# Massless Phases for the Villain model in $d\geq 3$

@article{Dario2020MasslessPF, title={Massless Phases for the Villain model in \$d\geq 3\$}, author={Paul Dario and Wei Wu}, journal={arXiv: Mathematical Physics}, year={2020} }

We consider the classical Villain rotator model in $\mathbb{Z}^d, d\geq 3$ at sufficiently low temperature, and prove that the truncated two-point function decays asymptotically as $|x|^{2-d}$, with an algebraic rate of convergence. We also obtain the same asymptotic decay separately for the transversal two-point functions. This quantifies the spontaneous magnetization result for the Villain model at low temperature, and rigorously establishes the Gaussian spin-wave conjecture in dimension $d…

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