Abstract
We investigate the phase diagram and the nature of the phase transitions of three-dimensional monopole-free models, characterized by a global symmetry, a gauge symmetry, and the absence of monopoles. We present numerical analyses based on Monte Carlo simulations for , 4, 10, 15, and 25. We observe a finite-temperature transition in all cases, related to the condensation of a local gauge-invariant order parameter. For we are unable to draw any definite conclusion on the nature of the transition. The results may be interpreted in terms of either a weak first-order transition or a continuous transition with anomalously large scaling corrections. However, the results allow us to exclude that the transition belongs to the vector universality class, as it occurs in the standard three-dimensional model without monopole suppression. For , the transition is of first order, and significantly weaker than that observed in the presence of monopoles. For the results are consistent with a conventional continuous transition. We compare our results with the existing literature and with the predictions of different field-theory approaches. They are consistent with the scenario in which the model undergoes continuous transitions for large values of , including , in agreement with analytic large- calculations for the -component Abelian-Higgs model.
7 More- Received 7 April 2020
- Accepted 4 June 2020
DOI:https://doi.org/10.1103/PhysRevE.101.062136
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