Criticality of O(N) symmetric models in the presence of discrete gauge symmetries

Abstract

We investigate the critical properties of the three-dimensional (3D) antiferromagnetic RP(N-1}) model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group (RG) flow of the most general Phi^4 theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_2 gauge symmetry.

12 pages. arXiv admin note: text overlap with arXiv:1502.07599, arXiv:1706.04365

References in corpus (4)

• The critical exponents of the superfluid transition in He4
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Three-dimensional antiferromagnetic CP(N-1) models
• Landau-Ginzburg-Wilson approach to critical phenomena in the presence of gauge symmetries

Cited by in corpus (13)

• Multicomponent compact Abelian-Higgs lattice models
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Bootstrapping traceless symmetric $O(N)$ scalars
• Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories
• Phases of SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions
• Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation
• Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality