Critical exponents of O(N) models in fractional dimensions

Abstract

We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In d=2 the N-dependence of the correlation length critical exponent gives us the last piece of information needed to establish a RG derivation of the Mermin-Wagner theorem. We also report critical exponents for multi-critical universality classes in the cases N>1 and N=0. Finally, in the large-N limit our critical exponents correctly approach those of the spherical model, allowing us to set N~100 as threshold for the quantitative validity of leading order large-N estimates.

6 pages, 5 figures, reference added

References in corpus (6)

• Exact evolution equation for the effective potential
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Scaling Solutions in Continuous Dimension
• Are there scaling solutions in the O(N)-models for large N in d>4?

Cited by in corpus (26)

• Long-range interacting quantum systems
• Multi-meson Yukawa interactions at criticality
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Anisotropic Long-Range Spin Systems
• Critical $O(N)$ models in the complex field plane
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Universal behavior of coupled order parameters below three dimensions
• Navigating through the O(N) archipelago
• Functional RG approach to the Potts model
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• The tricritical Ising CFT and conformal bootstrap
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• Universality in long-range interacting systems: the effective dimension approach
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Universal scaling in real dimension
• Renormalization Flow of Nonlinear Electrodynamics
• Nonperturbative treatment of a quenched Langevin field theory
• Renormalization of supersymmetric chiral theories in rational spacetime dimensions