Critical exponents of O(N) models in fractional dimensions

TL;DR

This paper calculates critical exponents for O(N) models across fractional dimensions and various N values, completing the RG classification and connecting to the Mermin-Wagner theorem, with implications for large-N approximations.

Contribution

It provides a comprehensive RG-based calculation of critical exponents for O(N) models in fractional dimensions and for continuous N, extending the universality class classification.

Findings

Critical exponents computed for fractional dimensions between 2 and 4.

Established RG derivation of the Mermin-Wagner theorem in 2D.

Large-N exponents approach spherical model results, with N~100 as a validity threshold.

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.