• Corpus ID: 252532174

Villain model with long-range couplings

@inproceedings{Giachetti2022VillainMW,
  title={Villain model with long-range couplings},
  author={Guido Giachetti and Nicol{\`o} Defenu and Stefano Ruffo and Andrea Trombettoni},
  year={2022}
}

• G. Giachetti, N. Defenu, +1 author A. Trombettoni
• Published 23 September 2022
• Physics

The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, σ , in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1 /r 2 interactions.