Critical quench dynamics of Wegner's $\mathbb{Z}_2$ gauge model: a geometric perspective
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918503754235904 |
|---|---|
| author | Agrawal, Ramgopal Cugliandolo, Leticia F. Picco, Marco |
| author_facet | Agrawal, Ramgopal Cugliandolo, Leticia F. Picco, Marco |
| contents | Wegner's $\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-size scaling analysis, we find that the critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent $z_{\rm p} \simeq 2.6$, consistent with that associated with the energy density, $z_{\rm c}$. Importantly, the value of $z_{\rm p}$ is robust with respect to the initial quench condition and the choice of geometrical objects. Furthermore, we provide a detailed characterization of the kinetics of different geometrical objects during the evolution from the percolation phase. Notably, we observe that the quench dynamics obeys dynamic scaling in terms of a growing lengthscale, $ξ_{\rm p}(t) \sim t^{1/z_{\rm p}}$, despite the absence of a local order parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical quench dynamics of Wegner's $\mathbb{Z}_2$ gauge model: a geometric perspective Agrawal, Ramgopal Cugliandolo, Leticia F. Picco, Marco Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory Wegner's $\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-size scaling analysis, we find that the critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent $z_{\rm p} \simeq 2.6$, consistent with that associated with the energy density, $z_{\rm c}$. Importantly, the value of $z_{\rm p}$ is robust with respect to the initial quench condition and the choice of geometrical objects. Furthermore, we provide a detailed characterization of the kinetics of different geometrical objects during the evolution from the percolation phase. Notably, we observe that the quench dynamics obeys dynamic scaling in terms of a growing lengthscale, $ξ_{\rm p}(t) \sim t^{1/z_{\rm p}}$, despite the absence of a local order parameter. |
| title | Critical quench dynamics of Wegner's $\mathbb{Z}_2$ gauge model: a geometric perspective |
| topic | Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.15841 |