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, sigma, 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 sigma < 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.

Villain model with long-range couplings / Giachetti, Guido; Defenu, Nicolò; Ruffo, Stefano; Trombettoni, Andrea. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2023:2(2023), pp. 1-24. [10.1007/jhep02(2023)238]

Villain model with long-range couplings

Giachetti, Guido;Ruffo, Stefano;Trombettoni, Andrea
2023-01-01

Abstract

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, sigma, 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 sigma < 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.
2023
2023
2
1
24
238
10.1007/jhep02(2023)238
https://link.springer.com/article/10.1007/JHEP02(2023)238
https://arxiv.org/abs/2209.11810
Giachetti, Guido; Defenu, Nicolò; Ruffo, Stefano; Trombettoni, Andrea
File in questo prodotto:
File Dimensione Formato  
JHEP02(2023)238.pdf

accesso aperto

Descrizione: pdf editoriale
Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 487.16 kB
Formato Adobe PDF
487.16 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/132091
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 1
social impact