Three-dimensional monopole-free CP${}^{N-1}$ models: Behavior in the presence of a quartic potential

Abstract

We investigate the phase diagram and the nature of the phase transitions in a three-dimensional model characterized by a global SU($N$) symmetry, a local U(1) symmetry, and the absence of monopoles. It represents a natural generalization of the gauge monopole-free (MF) CP${}^{N-1}$ model, in which the fixed-length constraint (London limit) is relaxed. We have performed Monte Carlo simulations for $N=2$ and 25, observing a finite-temperature transition in both cases, related to the condensation of a local gauge-invariant order parameter. For $N=2$ results for the MF model are consistent with a weak first-order transition. A continuous transition would be possible only if scaling corrections were anomalously large. For $N=25$ the results in the general MF model are also consistent with a first-order transition, that becomes weaker as the size of the field-length fluctuations decreases.

arXiv comment19 pages, 10 eps figures. arXiv admin note: text overlap with arXiv:2003.14075

References in corpus (25)

• Critical Phenomena and Renormalization-Group Theory
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum Field Theory in the Large N Limit: a review
• Deconfined quantum critical points: symmetries and dualities
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Quantum criticality with two length scales
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Fate of CP(N-1) fixed points with q-monopoles
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• 3D loop models and the CP^{n-1} sigma model
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Phase transitions in 3D loop models and the $C{P}^{n-1}$ $\sigma$ model
• Lattice Abelian-Higgs model with noncompact gauge fields
• 1/N Expansion for Critical Exponents of Magnetic Phase Transitions in CP^{N-1} Model at 2<d<4
• Consistent scaling exponents at the deconfined quantum-critical point
• Multicomponent compact Abelian-Higgs lattice models
• Three-dimensional ferromagnetic CP(N-1) models
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Large-N behavior of three-dimensional lattice CP(N-1) models
• Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory
• Berry phases, current lattices, and suppression of phase transitions in a lattice gauge theory of quantum antiferromagnets
• Three-dimensional monopole-free CP(N-1) models

Cited by in corpus (3)

• Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields
• Gauge fixing and gauge correlations in noncompact Abelian gauge models
• Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry