The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model

Résumé

With intensive Monte Carlo simulations and finite size scaling we undertake a percolation analysis of Wegner's three-dimensional $\mathbb{Z}_2$ lattice gauge model in equilibrium. We confirm that the loops threading excited plaquettes percolate at the thermal critical point $T_{\rm c}$ and we show that their critical exponents coincide with the ones of the loop representation of the dual 3D Ising model. We then construct Fortuin-Kasteleyn (FK) clusters using a random-cluster representation and find that they also percolate at $T_c$ and moreover give access to all thermal critical exponents. The Binder cumulants of the percolation order parameter of both loops and FK clusters demonstrate a pseudo first order transition. This study sheds light on the critical properties of quantum error correction and lattice gauge theories.

Dates et versions

hal-04730815 , version 1 (10-10-2024)

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Ramgopal Agrawal, Leticia F Cugliandolo, Lara Faoro, Lev B Ioffe, Marco Picco. The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model. 2024. ⟨hal-04730815⟩
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