The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model
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| Format: | Preprint |
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2024
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| _version_ | 1866911154232623104 |
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| author | Agrawal, Ramgopal Cugliandolo, Leticia F. Faoro, Lara Ioffe, Lev B. Picco, Marco |
| author_facet | Agrawal, Ramgopal Cugliandolo, Leticia F. Faoro, Lara Ioffe, Lev B. Picco, Marco |
| contents | After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a percolation analysis of Wegner's three-dimensional $\mathbb{Z}_2$ lattice gauge model using intensive Monte Carlo simulations and finite-size scaling, offering fresh insights into the topological phase transitions of gauge-invariant systems. We demonstrate that, regardless of the connection rules, geometrical loops, constructed by piercing excited plaquettes percolate precisely at the thermal critical point $T_{\rm c}$, with critical exponents coinciding with those of the loop representation of the dual 3D Ising model. Further, we construct Fortuin-Kasteleyn (FK) clusters in a random-cluster representation, showing that they also percolate at $T_{\rm c}$, enabling access to all thermal critical exponents. Strikingly, the Binder cumulants of the percolation order parameters for both loops and FK clusters reveal a pseudo-first-order transition. This work sheds new light on the critical behavior of pure LGTs, with potential implications for condensed matter systems and quantum error correction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_15123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model Agrawal, Ramgopal Cugliandolo, Leticia F. Faoro, Lara Ioffe, Lev B. Picco, Marco Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a percolation analysis of Wegner's three-dimensional $\mathbb{Z}_2$ lattice gauge model using intensive Monte Carlo simulations and finite-size scaling, offering fresh insights into the topological phase transitions of gauge-invariant systems. We demonstrate that, regardless of the connection rules, geometrical loops, constructed by piercing excited plaquettes percolate precisely at the thermal critical point $T_{\rm c}$, with critical exponents coinciding with those of the loop representation of the dual 3D Ising model. Further, we construct Fortuin-Kasteleyn (FK) clusters in a random-cluster representation, showing that they also percolate at $T_{\rm c}$, enabling access to all thermal critical exponents. Strikingly, the Binder cumulants of the percolation order parameters for both loops and FK clusters reveal a pseudo-first-order transition. This work sheds new light on the critical behavior of pure LGTs, with potential implications for condensed matter systems and quantum error correction. |
| title | The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model |
| topic | Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.15123 |