In this talk, I will present our work [1], in which we model the phase transition of a superconductor as a U(1) lattice gauge system, and determine its critical behavior. For this, we perform Monte Carlo simulations, treating the order parameter field and the gauge field on equal footing, without additional approximations. As the defining correlation function, we determine the order parameter correlation function including a gauge string, thus achieving a gauge-invariant characterization of the long-range behavior explicitly. We obtain a critical exponent that is consistent with the exponent of the U(1) transition of neutral bosons, i.e. of Bose-Einstein condensation. We determine the critical behavior of the heat capacity, which displays a temperature depends consistent with an XY transition. These results clarify the universality class of the phase transition of this system.

References
[1] G. S. Reese, L. Mathey, arXiv preprint arXiv:2603.09895 (2026)
* Acknowledgement(s): authors acknowledge support from the Cluster of Excellence 'CUI: Advanced Imaging of Matter' of the Deutsche Forschungsgemeinschaft (DFG) - EXC 2056 - project ID 390715994 and ERDF of the European Union and by ’Fonds of the Hamburg Ministry of Science, Research, Equalities and Districts (BWFGB)’.
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