Universality Class of $O(N)$ Models

Abstract

We point out that existing numerical data on the correlation length and magnetic susceptibility suggest that the two dimensional $O(3)$ model with standard action has critical exponent $\eta =1/4$, which is inconsistent with asymptotic freedom. This value of $\eta$ is also different from the one of the Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$ model at $\theta =\pi$.

8 pages, with 3 figures included, postscript. An error concerning the errors has been corrected

References in corpus (6)

• Finite-Size Scaling at $\xi /L\gg 1$
• Asymptotic Scaling in the Two-Dimensional $O(3)$ $\sigma$-Model at Correlation Length $10^5$
• Logarithmic Corrections to Scaling in the Two Dimensional $XY$--Model
• Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models
• Two-Dimensional $O(3)$ $\sigma$-Model up to Correlation Length $10^5$
• Nonuniformity of the $1/N$ Expansion for Two-Dimensional $O(N)$ Models

Cited by in corpus (22)

• The Kosterlitz-Thouless Universality Class
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
• High-Temperature Series Analysis of the Free Energy and Susceptibility of the 2D Random-Bond Ising Model
• Density of Partition Function Zeroes and Phase Transition Strength
• Quasi-long-range ordering in a finite-size 2D Heisenberg model
• On a microcanonical relation between continuous and discrete spin models
• Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories
• Topological Lattice Actions for the 2d XY Model
• Robustness of the O($N$) universality class
• Renormalization group approach for Lorentz-violating scalar field theory at all loop orders
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Quasi-asymptotic freedom in the two dimensional O(3) model
• All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method
• Numerical investigation of logarithmic corrections in two-dimensional spin models
• Diffeomorphism symmetry effect on the O(N ) universality class
• Density of states of continuous and discrete spin models: a case study
• Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders
• Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model
• Finite-size scaling of the helicity modulus of the two-dimensional O(3) model
• Influence of conformal symmetry on the amplitude ratios for O($N$) models
• NLO critical exponents of O($N$) lambda ${\varphi }^4$ scalar field theories in curved spacetime