High-accuracy critical exponents of O(N) hierarchical sigma models

TL;DR

This paper provides high-precision calculations of critical exponents for 3D O(N) hierarchical sigma models, confirming theoretical predictions and exploring 1/N expansion coefficients.

Contribution

It offers the most accurate numerical estimates of critical exponents for the 3D O(N) hierarchical model up to N=20, validating theoretical equations.

Findings

Critical exponents gamma and subleading exponents match Polchinski and Litim equations.

Critical temperatures for the nonlinear sigma model measure are calculated.

Potential extraction of 1/N expansion coefficients from data.

Abstract

We perform high-accuracy calculations of the critical exponent gamma and its subleading exponent for the 3D O(N) Dyson's hierarchical model, for N up to 20. We calculate the critical temperatures for the nonlinear sigma model measure. We discuss the possibility of extracting the first coefficients of the 1/N expansion from our numerical data. We show that the leading and subleading exponents agreewith Polchinski equation and the equivalent Litim equation, in the local potential approximation, with at least 4 significant digits.