Villain model with long-range couplings
OPEN ACCESS
Loading...
Author / Producer
Date
2023-02
Publication Type
Journal Article
ETH Bibliography
yes
Citations
Altmetric
OPEN ACCESS
Data
Rights / License
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, 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/r2 interactions.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
2023 (2)
Pages / Article No.
238
Publisher
Springer
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Phase Transitions; Spontaneous Symmetry Breaking; Lattice Integrable Models
Organisational unit
03355 - Graf, Gian Michele / Graf, Gian Michele