Critical quench dynamics of Wegner's ℤ2 gauge model: a geometric perspective
Abstract
Wegner's ℤ2 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 zp ≃ 2.6, consistent with that associated with the energy density, zc. Importantly, the value of zp 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, ξp(t) ∼ t1/zp, despite the absence of a local order parameter.
Versions
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BibTeX
@misc{agrawal2026critical,
title = {{Critical quench dynamics of Wegner's $\mathbbZ_2$ gauge model: a geometric perspective}},
author = {Ramgopal Agrawal and Leticia F. Cugliandolo and Marco Picco},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.15841},
eprint = {2605.15841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15841},
}
RIS
TY - UNPB
TI - Critical quench dynamics of Wegner's ℤ_2 gauge model: a geometric perspective
AU - Ramgopal Agrawal
AU - Leticia F. Cugliandolo
AU - Marco Picco
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2605.15841
UR - https://arxiv.org/abs/2605.15841
AB - Wegner's 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_p ≃ 2.6, consistent with that associated with the energy density, z_c. Importantly, the value of z_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_p(t) ∼ t^1/z_p, despite the absence of a local order parameter.
ER -