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Geometric Phase Transition of the Three-Dimensional Z_{2} Lattice Gauge Model
Ramgopal Agrawal1, Leticia F Cugliandolo1, Lara Faoro2
1Laboratoire de Physique Théorique et Hautes Energies, Sorbonne Université, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France.
Topological phase transitions in lattice gauge theories are revealed by percolating geometrical loops and Fortuin-Kasteleyn clusters at the critical temperature. This percolation analysis offers new insights into these complex systems.
Area of Science:
- High-energy physics
- Condensed matter physics
- Statistical mechanics
Background:
- Lattice gauge theories (LGTs) describe fundamental interactions but studying their topological phase transitions is difficult due to the lack of local order parameters.
- Fifty years of research have not fully resolved the nature of confinement-deconfinement transitions in LGTs.
Purpose of the Study:
- To investigate topological phase transitions in the 3D Z_{2} lattice gauge model using percolation analysis.
- To provide new insights into the critical behavior of gauge-invariant systems and their phase transitions.
Main Methods:
- Intensive Monte Carlo simulations and finite-size scaling were employed on Wegner's 3D Z_{2} lattice gauge model.
- Percolation analysis was performed on geometrical loops formed by excited plaquettes.
- Fortuin-Kasteleyn (FK) clusters were constructed in a random-cluster representation.
Main Results:
- Geometrical loops were found to percolate precisely at the thermal critical point (T_{c}).
- Critical exponents for loop percolation match those of the dual 3D Ising model.
- FK clusters also percolate at T_{c}, providing access to all thermal critical exponents.
- Binder cumulants indicated a pseudo-first-order phase transition for both loop and FK cluster percolation.
Conclusions:
- Percolation analysis offers a powerful tool to study topological phase transitions in pure lattice gauge theories.
- The findings provide a deeper understanding of critical phenomena in gauge systems.
- This research has potential applications in condensed matter systems and quantum error correction.
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