Three-dimensional monopole-free CPN1 models

Andrea Pelissetto and Ettore Vicari
Phys. Rev. E 101, 062136 – Published 22 June 2020

Abstract

We investigate the phase diagram and the nature of the phase transitions of three-dimensional monopole-free CPN1 models, characterized by a global U(N) symmetry, a U(1) gauge symmetry, and the absence of monopoles. We present numerical analyses based on Monte Carlo simulations for N=2, 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 N=2 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 O(3) vector universality class, as it occurs in the standard three-dimensional CP1 model without monopole suppression. For N=4,10,and15, the transition is of first order, and significantly weaker than that observed in the presence of monopoles. For N=25 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 N, including N=, in agreement with analytic large-N calculations for the N-component Abelian-Higgs model.

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  • Received 7 April 2020
  • Accepted 4 June 2020

DOI:https://doi.org/10.1103/PhysRevE.101.062136

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Andrea Pelissetto

  • Dipartimento di Fisica dell'Università di Roma Sapienza and Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Roma, Italy

Ettore Vicari

  • Dipartimento di Fisica dell'Università di Pisa and Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, I-56127 Pisa, Italy

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Vol. 101, Iss. 6 — June 2020

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