Long-range order in the vision-cone XY model comes from the cone-lattice coupling, not from non-reciprocity, and a symmetric variant shows an order-by-disorder transition.
The Kosterlitz-Thouless phase transition: an introduction for the intrepid student
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This is a set of notes recalling some of the most important results on the XY model from the ground up. They are meant for a junior researcher wanting to get accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D classical XY model. The connection to the 2D Coulomb gas is presented in detail, as well as the renormalization group flow obtained from this dual representation. A numerical Monte-Carlo approach to the classical XY model is presented. Finally, two physical setting that realize the celebrated Kosterlitz-Thouless phase transition are presented: superfluid and liquid crystal thin films.
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The XY model with vision cone: non-reciprocal vs. reciprocal interactions
Long-range order in the vision-cone XY model comes from the cone-lattice coupling, not from non-reciprocity, and a symmetric variant shows an order-by-disorder transition.